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Questions and Answers

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?

  • 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?

  • 5 litres (correct)
  • 10 litres
  • 7 litres
  • 3 litres

Convert 3 meters into millimeters.

<p>3,000 mm (D)</p> Signup and view all the answers

What is the area of a rectangle with a length of 12 cm and a width of 5 cm?

<p>60 $cm^2$ (A)</p> Signup and view all the answers

How many millilitres are there in 3.5 cups?

<p>875 ml (C)</p> Signup and view all the answers

Determine the volume of a rectangular box with length 8 m, breadth 5 m, and height 3 m.

<p>120 $m^3$ (B)</p> Signup and view all the answers

What is the circumference of a circle with a radius of 4 cm?

<p>25.12 cm (C)</p> Signup and view all the answers

Calculate the area of a triangle with a base of 10 cm and a perpendicular height of 6 cm.

<p>30 $cm^2$ (A)</p> Signup and view all the answers

Convert 5,500 grams (g) into kilograms (kg).

<p>5.5 kg (A)</p> Signup and view all the answers

A cylindrical tank has a radius of 2 meters and a height of 5 meters. What is its volume?

<p>62.8 $m^3$ (D)</p> Signup and view all the answers

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?

<p>$552 (A)</p> Signup and view all the answers

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?

<p>3 $m^3$ cement, 9 $m^3$ stone (D)</p> Signup and view all the answers

If 2 tablespoons of a medicine are required per day, how many days will a 500 ml bottle last?

<p>16.67 days (B)</p> Signup and view all the answers

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?

<p>58 $m^2$ (A)</p> Signup and view all the answers

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?

<p>Approximately 3,486 $m^2$ (D)</p> Signup and view all the answers

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?

<p>92 km/h (C)</p> Signup and view all the answers

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.

<p>Approximately 532.3 $cm^3$ (B)</p> Signup and view all the answers

Determine the number of 5 cm cubes that can fit inside a rectangular box with dimensions 20 cm x 30 cm x 40 cm.

<p>960 cubes (A)</p> Signup and view all the answers

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?

<p>1920 tiles (A)</p> Signup and view all the answers

What is the area equivalent of 5 $m^3$ in kilolitres?

<p>5 kilolitres (A)</p> Signup and view all the answers

A journey is planned using a travel timetable. What information does a travel timetable provide?

<p>Departure and arrival times (C)</p> Signup and view all the answers

If you need to convert 5 meters into centimeters, which operation should you perform?

<p>Multiply by 100 (C)</p> Signup and view all the answers

What is the perimeter of a rectangle with a length of 9 cm and a width of 6 cm?

<p>30 cm (C)</p> Signup and view all the answers

How many tablespoons are equal to 75 ml?

<p>5 (C)</p> Signup and view all the answers

What is the volume of a cylinder with a radius of 3 meters and a height of 7 meters?

<p>198 $m^3$ (A)</p> Signup and view all the answers

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?

<p>3 litres (B)</p> Signup and view all the answers

A bottle contains 1.5 liters of juice. If one serving is 250 ml, how many servings are in the bottle?

<p>6 (B)</p> Signup and view all the answers

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?

<p>21 cubic meters (D)</p> Signup and view all the answers

What is the area of a circle with a diameter of 14 cm?

<p>154 $cm^2$ (A)</p> Signup and view all the answers

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?

<p>8 meters (D)</p> Signup and view all the answers

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?

<p>88.26 $m^2$ (D)</p> Signup and view all the answers

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?

<p>96 km/h (C)</p> Signup and view all the answers

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?

<p>$753.60 (A)</p> Signup and view all the answers

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?

<p>391 tiles (C)</p> Signup and view all the answers

Calculate the total surface area of a cylinder (including both ends) with a radius of 5 cm and a height of 12 cm, using $Ï€ = 3.14$.

<p>534 $cm^2$ (D)</p> Signup and view all the answers

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.

<p>$1,924.75 (C)</p> Signup and view all the answers

A hemispherical tank has a radius of 6 meters. What is the volume of the tank?

<p>452.16 $m^3$ (A)</p> Signup and view all the answers

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?

<p>$1,575 (B)</p> Signup and view all the answers

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: $V = \frac{1}{3} \pi h (R^2 + Rr + r^2)$?

<p>712.34 $cm^3$ (A)</p> Signup and view all the answers

To convert from a larger unit of length to a smaller unit in the metric system, which operation should be performed?

<p>Multiplication (D)</p> Signup and view all the answers

How many millilitres are there in 2.5 litres?

<p>2,500 ml (A)</p> Signup and view all the answers

If a recipe calls for 2 cups of milk, what is the equivalent volume in millilitres?

<p>500 ml (A)</p> Signup and view all the answers

What is the perimeter of a triangle with sides measuring 5 cm, 7 cm, and 9 cm?

<p>21 cm (A)</p> Signup and view all the answers

A square has a side length of 10 cm. What is its area?

<p>100 cm (B)</p> Signup and view all the answers

What is the volume of a rectangular box with dimensions of 2 meters length, 1 meter breadth, and 2 meters height?

<p>4 m (C)</p> Signup and view all the answers

If 3 teaspoons are needed for a recipe, what is the equivalent amount in tablespoons?

<p>1 tablespoon (A)</p> Signup and view all the answers

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?

<p>7 litres (C)</p> Signup and view all the answers

Convert 3 cubic meters ($m^3$) into kilolitres (kl).

<p>3 kl (C)</p> Signup and view all the answers

What is the circumference of a circle with a radius of 5 cm? (Use 3.14)

<p>31.4 cm (B)</p> Signup and view all the answers

A rectangular garden is 12 meters long and 8 meters wide. What length of fencing is needed to enclose it?

<p>40 meters (C)</p> Signup and view all the answers

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?

<p>20 cubic meters (C)</p> Signup and view all the answers

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?

<p>120 km/h (C)</p> Signup and view all the answers

What is the area of a triangle with a base of 12 cm and a perpendicular height of 8 cm?

<p>48 cm (D)</p> Signup and view all the answers

A cylindrical tank has a radius of 3 meters and a height of 4 meters. What is its volume? (Use 3.14)

<p>113.04 m (A)</p> Signup and view all the answers

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?

<p>160 tiles (A)</p> Signup and view all the answers

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)

<p>42.24 m (D)</p> Signup and view all the answers

A hemispherical tank has a radius of 4 meters. What is the volume of the tank? (Use 3.14)

<p>133.97 m (C)</p> Signup and view all the answers

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)

<p>732.67 cm (A)</p> Signup and view all the answers

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)

<p>4563 m (A)</p> Signup and view all the answers

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?

<p>4 hours and 15 minutes (A)</p> Signup and view all the answers

If you need to convert 7 kilograms (kg) into grams (g), which operation should you perform and by what factor?

<p>Multiply by 1,000 (B)</p> Signup and view all the answers

Flashcards

How many centimetres equals 1 metre (m)?

100 centimetres (cm)

How many metres equals 1 kilometre (km)?

1,000 metres (m)

Convert to a smaller unit (metric)?

Multiply

Convert to a larger unit (metric)?

Divide

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How many millilitres equals 1 litre (l)?

1,000 millilitres (ml)

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Definition: How many litres equals 1 kilolitre (kl)?

1,000 litres (l)

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How many milligrams equals 1 gram (g)?

1,000 milligrams (mg)

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How many grams equals 1 kilogram (kg)?

1,000 grams (g)

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How many kilograms equals 1 tonne (t)?

1,000 kilograms (kg)

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How many ml in 1 cup (cooking)?

250 ml

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How many ml in 1 tablespoon (tbsp)?

15 ml

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How many ml in 1 teaspoon (tsp)?

5 ml

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How many ml in 1 cm³?

1 ml

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How many litres in 1,000 ml?

1 l

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What is Perimeter?

Total length of a shape's outer boundary.

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Rectangle Perimeter Formula

Perimeter = 2 × (length + width)

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Square Perimeter Formula

Perimeter = 4 × side

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Triangle Perimeter Formula

Perimeter = side 1 + side 2 + side 3

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Rectangle Area Formula

Area = length × width

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Circle Area Formula

Area = π × radius²

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Travel Timetables

Resources showing departure and arrival times for transport.

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Building Conversions

Ratio used to find cement, sand, and stone needs.

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Perimeter

Total distance around the outside of a 2D shape.

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Area

The amount of surface a 2D shape covers.

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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

The amount of space an object occupies.

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Rectangular Box Volume

Volume = length × breadth × height

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Cylinder Volume

Volume = π × radius² × height

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Combining Shapes

Divide complex shapes into simpler ones, then sum areas.

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Perimeter

The continuous line that forms the boundary of a closed geometric figure

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Triangle Area Formula

Area = 1/2 × base × perpendicular height

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Volume Units

Volume is expressed in cubic units such as mm³, cm³, m³, or km³.

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Unit Consistency

Ensure all measurements are in the same units before calculating volume.

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Spread Rate

Amount of liquid needed to cover a surface.

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Tide Timetables

For seaside locations, these show high and low tide times.

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Route Maps

These show stations/stops and routes.

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Fare Tables

These show the cost of travel options.

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Circumference

The distance around a circle.

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Circle Circumference Formula

Circumference = π × diameter

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Estimating Lengths

Using common things to guess lengths.

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Importance of Perimeter

Shows perimeter's importance for material needs.

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Foundation Volume

When calculating the volume of a foundation, use the rectangular box formula: Volume = length × breadth × height to determine how much concrete is needed.

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Volume Cost

Multiply the volume by the price per cubic meter to determine cost.

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Volume for composite shapes

Add individual volumes for the total.

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Volume for Containers

Calculating volume to determine container capacity.

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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 or Perimeter = 2 × (length + width)

Perimeter: Square

  • Perimeter = 4 × side length or Perimeter = 4 × side

Perimeter: Triangle

  • Perimeter = length of side 1 + length of side 2 + length of side 3 or Perimeter = side 1 + side 2 + side 3

Perimeter: Circle

  • Circumference = Ï€ × diameter or Circumference = 2 × Ï€ × 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 = Ï€ × 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 = Ï€ × radius² × height

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