Podcast
Questions and Answers
How many litres are equivalent to 5 kilolitres?
How many litres are equivalent to 5 kilolitres?
- 5,000 litres (correct)
- 50,000 litres
- 50 litres
- 500 litres
What is the perimeter of a square with a side length of 7 cm?
What is the perimeter of a square with a side length of 7 cm?
- 28 cm (correct)
- 14 cm
- 21 cm
- 49 cm
If a wall has an area of 35 $m^2$ and the paint spread rate is 7 $m^2$ per litre, how many litres of paint are needed?
If a wall has an area of 35 $m^2$ and the paint spread rate is 7 $m^2$ per litre, how many litres of paint are needed?
- 5 litres (correct)
- 10 litres
- 7 litres
- 3 litres
Convert 3 meters into millimeters.
Convert 3 meters into millimeters.
What is the area of a rectangle with a length of 12 cm and a width of 5 cm?
What is the area of a rectangle with a length of 12 cm and a width of 5 cm?
How many millilitres are there in 3.5 cups?
How many millilitres are there in 3.5 cups?
Determine the volume of a rectangular box with length 8 m, breadth 5 m, and height 3 m.
Determine the volume of a rectangular box with length 8 m, breadth 5 m, and height 3 m.
What is the circumference of a circle with a radius of 4 cm?
What is the circumference of a circle with a radius of 4 cm?
Calculate the area of a triangle with a base of 10 cm and a perpendicular height of 6 cm.
Calculate the area of a triangle with a base of 10 cm and a perpendicular height of 6 cm.
Convert 5,500 grams (g) into kilograms (kg).
Convert 5,500 grams (g) into kilograms (kg).
A cylindrical tank has a radius of 2 meters and a height of 5 meters. What is its volume?
A cylindrical tank has a radius of 2 meters and a height of 5 meters. What is its volume?
You need to fence a rectangular garden that measures 15 meters in length and 8 meters in width. If fencing costs $12 per meter, what will be the total cost?
You need to fence a rectangular garden that measures 15 meters in length and 8 meters in width. If fencing costs $12 per meter, what will be the total cost?
For a construction project, the ratio of cement to sand to stone is 1:2:3. If 6 cubic meters of sand are used, how much cement and stone are required?
For a construction project, the ratio of cement to sand to stone is 1:2:3. If 6 cubic meters of sand are used, how much cement and stone are required?
If 2 tablespoons of a medicine are required per day, how many days will a 500 ml bottle last?
If 2 tablespoons of a medicine are required per day, how many days will a 500 ml bottle last?
A composite shape consists of a rectangle (8 m x 5 m) and a triangle (base 6 m, height 4 m) on top of it. What is the total area of the composite shape?
A composite shape consists of a rectangle (8 m x 5 m) and a triangle (base 6 m, height 4 m) on top of it. What is the total area of the composite shape?
You have a plot of land that measures 50 meters by 80 meters. You want to build a circular pool with a diameter of 20 meters. How much area of your land will be left after the pool is built?
You have a plot of land that measures 50 meters by 80 meters. You want to build a circular pool with a diameter of 20 meters. How much area of your land will be left after the pool is built?
Given a travel timetable, a train departs Station A at 08:45 and arrives at Station B at 11:20. The distance between the stations is 250 km. What is the average speed of the train in km/h, rounded to the nearest whole number?
Given a travel timetable, a train departs Station A at 08:45 and arrives at Station B at 11:20. The distance between the stations is 250 km. What is the average speed of the train in km/h, rounded to the nearest whole number?
Calculate the volume of a truncated cone with a base radius of 5 cm, a top radius of 3 cm, and a height of 8 cm. Use the formula: $V = \frac{1}{3}\pi h (R^2 + Rr + r^2)$ where R = base radius, r = top radius, and h = height.
Calculate the volume of a truncated cone with a base radius of 5 cm, a top radius of 3 cm, and a height of 8 cm. Use the formula: $V = \frac{1}{3}\pi h (R^2 + Rr + r^2)$ where R = base radius, r = top radius, and h = height.
Determine the number of 5 cm cubes that can fit inside a rectangular box with dimensions 20 cm x 30 cm x 40 cm.
Determine the number of 5 cm cubes that can fit inside a rectangular box with dimensions 20 cm x 30 cm x 40 cm.
You are tiling a floor with dimensions 6.4 meters in length and 4.8 meters in width. You are using square tiles that measure 40 cm x 40 cm. How many tiles are required to cover the entire floor?
You are tiling a floor with dimensions 6.4 meters in length and 4.8 meters in width. You are using square tiles that measure 40 cm x 40 cm. How many tiles are required to cover the entire floor?
What is the area equivalent of 5 $m^3$ in kilolitres?
What is the area equivalent of 5 $m^3$ in kilolitres?
A journey is planned using a travel timetable. What information does a travel timetable provide?
A journey is planned using a travel timetable. What information does a travel timetable provide?
If you need to convert 5 meters into centimeters, which operation should you perform?
If you need to convert 5 meters into centimeters, which operation should you perform?
What is the perimeter of a rectangle with a length of 9 cm and a width of 6 cm?
What is the perimeter of a rectangle with a length of 9 cm and a width of 6 cm?
How many tablespoons are equal to 75 ml?
How many tablespoons are equal to 75 ml?
What is the volume of a cylinder with a radius of 3 meters and a height of 7 meters?
What is the volume of a cylinder with a radius of 3 meters and a height of 7 meters?
If the spread rate of a paint is 8 $m^2$ per litre, how many litres of paint are needed to cover a wall that is 4 meters high and 6 meters long?
If the spread rate of a paint is 8 $m^2$ per litre, how many litres of paint are needed to cover a wall that is 4 meters high and 6 meters long?
A bottle contains 1.5 liters of juice. If one serving is 250 ml, how many servings are in the bottle?
A bottle contains 1.5 liters of juice. If one serving is 250 ml, how many servings are in the bottle?
For a building project, the ratio of cement to sand is 1:3. If 7 cubic meters of cement are used, how much sand is required?
For a building project, the ratio of cement to sand is 1:3. If 7 cubic meters of cement are used, how much sand is required?
What is the area of a circle with a diameter of 14 cm?
What is the area of a circle with a diameter of 14 cm?
You want to build a rectangular garden with an area of 48 $m^2$. If one side is 6 meters long, what is the length of the adjacent side?
You want to build a rectangular garden with an area of 48 $m^2$. If one side is 6 meters long, what is the length of the adjacent side?
A composite shape consists of a rectangle (10 m x 6 m) and a semicircle on one of its shorter sides. What is the approximate total area of the composite shape?
A composite shape consists of a rectangle (10 m x 6 m) and a semicircle on one of its shorter sides. What is the approximate total area of the composite shape?
A train travels from Station A to Station B, a distance of 320 km. It departs Station A at 09:15 and arrives at Station B at 12:35. What is the average speed of the train in km/h?
A train travels from Station A to Station B, a distance of 320 km. It departs Station A at 09:15 and arrives at Station B at 12:35. What is the average speed of the train in km/h?
You have a cylindrical tank with a radius of 4 meters and a height of 6 meters. If you want to fill it with water, and the water costs $2.50 per cubic meter, what will be the total cost to fill the tank?
You have a cylindrical tank with a radius of 4 meters and a height of 6 meters. If you want to fill it with water, and the water costs $2.50 per cubic meter, what will be the total cost to fill the tank?
A room is being tiled with square tiles measuring 20 cm x 20 cm. The room is 4.6 meters long and 3.4 meters wide. How many tiles are needed to cover the entire floor?
A room is being tiled with square tiles measuring 20 cm x 20 cm. The room is 4.6 meters long and 3.4 meters wide. How many tiles are needed to cover the entire floor?
Calculate the total surface area of a cylinder (including both ends) with a radius of 5 cm and a height of 12 cm, using $Ï€ = 3.14$.
Calculate the total surface area of a cylinder (including both ends) with a radius of 5 cm and a height of 12 cm, using $Ï€ = 3.14$.
You're designing a garden consisting of circular and rectangular sections. The rectangular section measures 15 meters in length and 10 meters in width. The circular section has a diameter of 7 meters and is placed adjacent to the rectangle. If you need to cover the entire garden with mulch costing $10 per square meter, calculate the total cost for mulching the entire garden area.
You're designing a garden consisting of circular and rectangular sections. The rectangular section measures 15 meters in length and 10 meters in width. The circular section has a diameter of 7 meters and is placed adjacent to the rectangle. If you need to cover the entire garden with mulch costing $10 per square meter, calculate the total cost for mulching the entire garden area.
A hemispherical tank has a radius of 6 meters. What is the volume of the tank?
A hemispherical tank has a radius of 6 meters. What is the volume of the tank?
Imagine you're tiling a floor in an oddly shaped room formed by a rectangle and a right-angled triangle. The rectangle measures 8 meters by 6 meters, and the triangle has a base of 5 meters and a height of 6 meters extending from one of the rectangle’s longer sides. If the tiles cost $25 per square meter, how much would it cost to tile the entire floor?
Imagine you're tiling a floor in an oddly shaped room formed by a rectangle and a right-angled triangle. The rectangle measures 8 meters by 6 meters, and the triangle has a base of 5 meters and a height of 6 meters extending from one of the rectangle’s longer sides. If the tiles cost $25 per square meter, how much would it cost to tile the entire floor?
What is the calculated volume of a frustum of a cone (a truncated cone) given a top radius of 4 cm, a base radius of 7 cm, and a height of 9 cm using the formula: $V = \frac{1}{3} \pi h (R^2 + Rr + r^2)$?
What is the calculated volume of a frustum of a cone (a truncated cone) given a top radius of 4 cm, a base radius of 7 cm, and a height of 9 cm using the formula: $V = \frac{1}{3} \pi h (R^2 + Rr + r^2)$?
To convert from a larger unit of length to a smaller unit in the metric system, which operation should be performed?
To convert from a larger unit of length to a smaller unit in the metric system, which operation should be performed?
How many millilitres are there in 2.5 litres?
How many millilitres are there in 2.5 litres?
If a recipe calls for 2 cups of milk, what is the equivalent volume in millilitres?
If a recipe calls for 2 cups of milk, what is the equivalent volume in millilitres?
What is the perimeter of a triangle with sides measuring 5 cm, 7 cm, and 9 cm?
What is the perimeter of a triangle with sides measuring 5 cm, 7 cm, and 9 cm?
A square has a side length of 10 cm. What is its area?
A square has a side length of 10 cm. What is its area?
What is the volume of a rectangular box with dimensions of 2 meters length, 1 meter breadth, and 2 meters height?
What is the volume of a rectangular box with dimensions of 2 meters length, 1 meter breadth, and 2 meters height?
If 3 teaspoons are needed for a recipe, what is the equivalent amount in tablespoons?
If 3 teaspoons are needed for a recipe, what is the equivalent amount in tablespoons?
A painter needs to cover a wall with an area of 42 $m^2$. If the paint has a spread rate of 6 $m^2$ per litre, how many litres of paint are required?
A painter needs to cover a wall with an area of 42 $m^2$. If the paint has a spread rate of 6 $m^2$ per litre, how many litres of paint are required?
Convert 3 cubic meters ($m^3$) into kilolitres (kl).
Convert 3 cubic meters ($m^3$) into kilolitres (kl).
What is the circumference of a circle with a radius of 5 cm? (Use 3.14)
What is the circumference of a circle with a radius of 5 cm? (Use 3.14)
A rectangular garden is 12 meters long and 8 meters wide. What length of fencing is needed to enclose it?
A rectangular garden is 12 meters long and 8 meters wide. What length of fencing is needed to enclose it?
For a concrete mixture, the ratio of cement to sand to gravel is 1:2:4. If 5 cubic meters of cement are used, how much gravel is required?
For a concrete mixture, the ratio of cement to sand to gravel is 1:2:4. If 5 cubic meters of cement are used, how much gravel is required?
A train departs Station X at 10:30 and arrives at Station Y at 13:00. If the distance between the stations is 300 km, what is the average speed of the train in km/h?
A train departs Station X at 10:30 and arrives at Station Y at 13:00. If the distance between the stations is 300 km, what is the average speed of the train in km/h?
What is the area of a triangle with a base of 12 cm and a perpendicular height of 8 cm?
What is the area of a triangle with a base of 12 cm and a perpendicular height of 8 cm?
A cylindrical tank has a radius of 3 meters and a height of 4 meters. What is its volume? (Use 3.14)
A cylindrical tank has a radius of 3 meters and a height of 4 meters. What is its volume? (Use 3.14)
A room is 5 meters long and 4 meters wide. You want to tile the floor with square tiles of side length 50 cm. How many tiles are needed?
A room is 5 meters long and 4 meters wide. You want to tile the floor with square tiles of side length 50 cm. How many tiles are needed?
A composite shape consists of a rectangle (6 m x 4 m) and a semicircle on one of its longer sides. What is the approximate total area of the composite shape? (Use 3.14)
A composite shape consists of a rectangle (6 m x 4 m) and a semicircle on one of its longer sides. What is the approximate total area of the composite shape? (Use 3.14)
A hemispherical tank has a radius of 4 meters. What is the volume of the tank? (Use 3.14)
A hemispherical tank has a radius of 4 meters. What is the volume of the tank? (Use 3.14)
Calculate the volume of a frustum of a cone with a base radius of 6 cm, a top radius of 4 cm, and a height of 10 cm. Use the formula: $V = rac{1}{3} \pi h (R^2 + Rr + r^2)$, where R = base radius, r = top radius, and h = height. (Use 3.14)
Calculate the volume of a frustum of a cone with a base radius of 6 cm, a top radius of 4 cm, and a height of 10 cm. Use the formula: $V = rac{1}{3} \pi h (R^2 + Rr + r^2)$, where R = base radius, r = top radius, and h = height. (Use 3.14)
You have a plot of land measuring 60 meters by 90 meters. You want to build a circular swimming pool with a diameter of 30 meters. Approximately how much area of your land will be left after the pool is built? (Use 3.14)
You have a plot of land measuring 60 meters by 90 meters. You want to build a circular swimming pool with a diameter of 30 meters. Approximately how much area of your land will be left after the pool is built? (Use 3.14)
A travel timetable shows a train departing at 09:55 and arriving at 14:10. What is the duration of the journey in hours and minutes?
A travel timetable shows a train departing at 09:55 and arriving at 14:10. What is the duration of the journey in hours and minutes?
If you need to convert 7 kilograms (kg) into grams (g), which operation should you perform and by what factor?
If you need to convert 7 kilograms (kg) into grams (g), which operation should you perform and by what factor?
Flashcards
How many centimetres equals 1 metre (m)?
How many centimetres equals 1 metre (m)?
100 centimetres (cm)
How many metres equals 1 kilometre (km)?
How many metres equals 1 kilometre (km)?
1,000 metres (m)
Convert to a smaller unit (metric)?
Convert to a smaller unit (metric)?
Multiply
Convert to a larger unit (metric)?
Convert to a larger unit (metric)?
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How many millilitres equals 1 litre (l)?
How many millilitres equals 1 litre (l)?
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Definition: How many litres equals 1 kilolitre (kl)?
Definition: How many litres equals 1 kilolitre (kl)?
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How many milligrams equals 1 gram (g)?
How many milligrams equals 1 gram (g)?
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How many grams equals 1 kilogram (kg)?
How many grams equals 1 kilogram (kg)?
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How many kilograms equals 1 tonne (t)?
How many kilograms equals 1 tonne (t)?
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How many ml in 1 cup (cooking)?
How many ml in 1 cup (cooking)?
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How many ml in 1 tablespoon (tbsp)?
How many ml in 1 tablespoon (tbsp)?
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How many ml in 1 teaspoon (tsp)?
How many ml in 1 teaspoon (tsp)?
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How many ml in 1 cm³?
How many ml in 1 cm³?
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How many litres in 1,000 ml?
How many litres in 1,000 ml?
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What is Perimeter?
What is Perimeter?
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Rectangle Perimeter Formula
Rectangle Perimeter Formula
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Square Perimeter Formula
Square Perimeter Formula
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Triangle Perimeter Formula
Triangle Perimeter Formula
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Rectangle Area Formula
Rectangle Area Formula
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Circle Area Formula
Circle Area Formula
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Travel Timetables
Travel Timetables
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Building Conversions
Building Conversions
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Perimeter
Perimeter
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Area
Area
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Square Area Formula
Square Area Formula
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Triangle Area Formula
Triangle Area Formula
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Volume
Volume
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Rectangular Box Volume
Rectangular Box Volume
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Cylinder Volume
Cylinder Volume
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Combining Shapes
Combining Shapes
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Perimeter
Perimeter
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Triangle Area Formula
Triangle Area Formula
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Volume Units
Volume Units
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Unit Consistency
Unit Consistency
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Spread Rate
Spread Rate
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Tide Timetables
Tide Timetables
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Route Maps
Route Maps
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Fare Tables
Fare Tables
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Circumference
Circumference
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Circle Circumference Formula
Circle Circumference Formula
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Estimating Lengths
Estimating Lengths
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Importance of Perimeter
Importance of Perimeter
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Foundation Volume
Foundation Volume
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Volume Cost
Volume Cost
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Volume for composite shapes
Volume for composite shapes
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Volume for Containers
Volume for Containers
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Study Notes
- These notes cover measurement, conversions, perimeter and area, and volume.
Metric Conversions: Length
- 10 millimeters (mm) equals 1 centimeter (cm).
- 100 centimeters (cm) equals 1 meter (m).
- 1,000 millimeters (mm) equals 1 meter (m).
- 1,000 meters (m) equals 1 kilometer (km).
- Multiply when converting to a smaller unit.
- Divide when converting to a larger unit.
Metric Conversions: Volume
- 1,000 milliliters (ml) equals 1 liter (l).
- 1,000 liters (l) equals 1 kiloliter (kl).
- Multiply when converting to a smaller unit.
- Divide when converting to a larger unit.
Metric Conversions: Weight
- 1,000 milligrams (mg) equals 1 gram (g).
- 1,000 grams (g) equals 1 kilogram (kg).
- 1,000 kilograms (kg) equals 1 tonne (t).
- Multiply when converting to a smaller unit.
- Divide when converting to a larger unit.
Cooking Conversions
- 1 cup equals 250 ml.
- 1 tablespoon (tbsp) equals 15 ml.
- 1 teaspoon (tsp) equals 5 ml.
Calculated Volume to Liquid Volume Conversions
- 1 cm³ equals 1 ml.
- 1,000 ml equals 1 l.
- 1 m³ equals 1 kl.
Calculated Area to Liquid Volume Conversions
- Area is calculated in square units (cm², mm², m²).
- Spread rate is used to calculate the volume of liquid needed to cover a surface.
Building Conversions
- Ratios determine the quantities for construction materials.
Travel Timetables and Tide Tables
- Travel timetables show departure and arrival times for transport.
- Route maps show stations/stops and routes.
- Fare tables show the cost of travel options.
- Tide timetables show high and low tide times.
Perimeter
- Perimeter is the total length of the outside of a shape.
- Perimeter is measured in millimeters (mm), centimeters (cm), meters (m), or kilometers (km).
- Perimeter is calculated by adding together the lengths of each side of a shape
Perimeter: Rectangle
Perimeter = 2 × length + 2 × width
orPerimeter = 2 × (length + width)
Perimeter: Square
Perimeter = 4 × side length
orPerimeter = 4 × side
Perimeter: Triangle
Perimeter = length of side 1 + length of side 2 + length of side 3
orPerimeter = side 1 + side 2 + side 3
Perimeter: Circle
Circumference = π × diameter
orCircumference = 2 × π × radius
Area
- Area measures the extent of a two-dimensional surface within a boundary and is measured in square units like cm², m², etc
Area: Rectangle
Area = length × width
Area: Square
Area = side × side = side²
Area: Triangle
Area = 1/2 × base × perpendicular height
Area: Circle
Area = π × radius²
Estimating Perimeter and Area
- Estimating lengths and distances can be achieved using common objects or body measurements.
Combining Shapes
- Break down complex shapes into simpler shapes to calculate the area.
Volume
- Volume measures the amount of space inside a 3-dimensional object and is expressed in cubic units such as mm³, cm³, m³, or km³.
Volume: Rectangular Box (Prism)
Volume = length × breadth × height
Volume: Cylinder
Volume = π × radius² × height
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