Podcast
Questions and Answers
What is the volume of juice that the cylindrical vessel can hold?
What is the volume of juice that the cylindrical vessel can hold?
- 2250π cm³
- 720π cm³
- 1440π cm³ (correct)
- 1800π cm³
How many glasses of juice are sold from the cylindrical vessel?
How many glasses of juice are sold from the cylindrical vessel?
- 110
- 100 (correct)
- 120
- 90
What is the total amount received by the stall keeper when each glass is sold for `15?
What is the total amount received by the stall keeper when each glass is sold for `15?
- `1500 (correct)
- `1200
- `1650
- `1350
What is the circumference of the base of the cylindrical vessel?
What is the circumference of the base of the cylindrical vessel?
What is the height of the cylindrical vessel that can hold a certain amount of water?
What is the height of the cylindrical vessel that can hold a certain amount of water?
If the lateral surface area of a cylinder is 94.2 cm² and its height is 5 cm, what is the radius of its base?
If the lateral surface area of a cylinder is 94.2 cm² and its height is 5 cm, what is the radius of its base?
What shape of cone is specifically being discussed in this chapter?
What shape of cone is specifically being discussed in this chapter?
What does cutting out the paper cone along its side allow you to see?
What does cutting out the paper cone along its side allow you to see?
What is the relationship between the curved portion of Fig. 13.15 (c) and the circular base of the cone?
What is the relationship between the curved portion of Fig. 13.15 (c) and the circular base of the cone?
What shape do the cut portions of the paper resemble?
What shape do the cut portions of the paper resemble?
What formula is used to calculate the area of each triangle from the paper cone?
What formula is used to calculate the area of each triangle from the paper cone?
What does the circumference of the base of a cone represent?
What does the circumference of the base of a cone represent?
In a village with a population of 4000, each person requires 150 litres of water per day. If the village has a tank measuring 20 m x 15 m x 6 m, for how many days will the water in the tank last?
In a village with a population of 4000, each person requires 150 litres of water per day. If the village has a tank measuring 20 m x 15 m x 6 m, for how many days will the water in the tank last?
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side length of the new cube?
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side length of the new cube?
A river is 3 m deep and 40 m wide, flowing at 2 km per hour. How much water, in cubic meters, will fall into the sea in a minute?
A river is 3 m deep and 40 m wide, flowing at 2 km per hour. How much water, in cubic meters, will fall into the sea in a minute?
If a cuboidal tank has a length of 2.5 m and depth of 10 m, and its capacity is 50000 litres, what is the breadth of the tank?
If a cuboidal tank has a length of 2.5 m and depth of 10 m, and its capacity is 50000 litres, what is the breadth of the tank?
A godown measures 40 m x 25 m x 15 m. What is the maximum number of wooden crates, each measuring 1.5 m x 1.25 m x 0.5 m, that can be stored in the godown?
A godown measures 40 m x 25 m x 15 m. What is the maximum number of wooden crates, each measuring 1.5 m x 1.25 m x 0.5 m, that can be stored in the godown?
What is the formula to calculate the volume of a cylinder?
What is the formula to calculate the volume of a cylinder?
What is the cost of white-washing the inside of the dome?
What is the cost of white-washing the inside of the dome?
What is the surface area of one iron sphere if the total surface area S of 27 spheres is melted to form a new sphere?
What is the surface area of one iron sphere if the total surface area S of 27 spheres is melted to form a new sphere?
What is the volume of the air inside the dome?
What is the volume of the air inside the dome?
What is the radius r′ of the new sphere formed by melting 27 solid iron spheres?
What is the radius r′ of the new sphere formed by melting 27 solid iron spheres?
What is the ratio of the surface area S to the new surface area S′ of the sphere formed by melting 27 solid iron spheres?
What is the ratio of the surface area S to the new surface area S′ of the sphere formed by melting 27 solid iron spheres?
How much medicine (in mm³) is needed to fill a capsule in the shape of a sphere with a diameter of 3.5 mm?
How much medicine (in mm³) is needed to fill a capsule in the shape of a sphere with a diameter of 3.5 mm?
What is the relationship between the volume of a sphere and the volume of water displaced by it?
What is the relationship between the volume of a sphere and the volume of water displaced by it?
What conclusion can be drawn from the repeated experiments with spheres of varying radii?
What conclusion can be drawn from the repeated experiments with spheres of varying radii?
What is the formula for finding the volume of a hemisphere?
What is the formula for finding the volume of a hemisphere?
What is the volume of a sphere of radius 11.2 cm?
What is the volume of a sphere of radius 11.2 cm?
If a metallic shot-putt is a sphere of radius 4.9 cm, what would be its mass if the density of the metal is 7.8 g per cm³?
If a metallic shot-putt is a sphere of radius 4.9 cm, what would be its mass if the density of the metal is 7.8 g per cm³?
What does the formula $V = \frac{4}{3} \pi r^3$ represent in relation to a sphere?
What does the formula $V = \frac{4}{3} \pi r^3$ represent in relation to a sphere?
Flashcards are hidden until you start studying
Study Notes
Cylindrical Vessel
- The volume of juice that the cylindrical vessel can hold is unknown.
- It can hold an unknown number of glasses of juice, each selling for ₹15.
Cylinder Properties
- The circumference of the base of the cylindrical vessel is unknown.
- The height of the cylindrical vessel that can hold a certain amount of water is unknown.
- If the lateral surface area of a cylinder is 94.2 cm² and its height is 5 cm, the radius of its base is unknown.
Cones
- The shape of cone being discussed is a paper cone.
- Cutting out the paper cone along its side allows you to see the relationship between the curved portion and the circular base of the cone.
- The curved portion of Fig. 13.15 (c) is related to the circular base of the cone.
- The cut portions of the paper resemble a rectangle.
- The formula to calculate the area of each triangle from the paper cone is unknown.
Circumference and Base of a Cone
- The circumference of the base of a cone represents the perimeter of the circular base.
Real-World Applications
- In a village with a population of 4000, each person requires 150 litres of water per day.
- A tank measuring 20 m x 15 m x 6 m can hold water for an unknown number of days.
Solids
- A solid cube of side 12 cm cut into eight cubes of equal volume will have a new cube with a side length of unknown.
- A cuboidal tank with a length of 2.5 m, depth of 10 m, and capacity of 50000 litres has a breadth of unknown.
- A godown measuring 40 m x 25 m x 15 m can store an unknown number of wooden crates, each measuring 1.5 m x 1.25 m x 0.5 m.
Formulas
- The formula to calculate the volume of a cylinder is unknown.
Spheres
- The cost of white-washing the inside of the dome is unknown.
- The surface area of one iron sphere is related to the total surface area S of 27 spheres melted to form a new sphere.
- The volume of the air inside the dome is unknown.
- The radius r′ of the new sphere formed by melting 27 solid iron spheres is unknown.
- The ratio of the surface area S to the new surface area S′ of the sphere formed by melting 27 solid iron spheres is unknown.
- The formula $V = \frac{4}{3} \pi r^3$ represents the volume of a sphere.
Hemisphere and Sphere
- The formula for finding the volume of a hemisphere is unknown.
- The volume of a sphere of radius 11.2 cm is unknown.
- A metallic shot-putt with a radius of 4.9 cm has a mass of unknown if the density of the metal is 7.8 g per cm³.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
