CBSE Class 10 Maths Chapter 12 Surface Areas and Volumes Competency-Focused Practice Questions With Answer Key 2024-25: Free PDF Download

Multiple Choice Question

Q:1 The table below shows the measurements of 3 right circular cones.

Which of these have the same curved surface area?

1 only P and Q 

2 only Q and R 

3 only R and P 

4 (P, Q and R have different curved surface areas because they have different radii and slant heights) 

Free Response Questions

Q:2 State whether the following statement is true or false. Explain your answer. 

If a cylinder and a cone have equal radii and equal volume, then the height of the cylinder is 3 times that of the cone. 

Q:3 Two solid hemispheres are joined together to make a sphere. 

The total surface area of the sphere is __________ the sum of the total surface areas of the hemispheres. Fill in the blank and give a valid reason. 

Q:4 Shown below is a flask comprising of a cylinder on top of a frustum. In a tilted position, the height of the liquid is marked.

Write an expression for height of the liquid when the flask is in upright position.

Q:5 Vidit is a designer who had printed a 23 cm by 4.5 cm rectangular label. He is now 3D printing a cylindrical water bottle for the label. He wants the label to be wrapped around the bottle such that there is an overlap of 1 cm for sticking.

(Note: The figures are not to scale.) 

What should be the radius of the water bottle? Show your work.

 (Note: Take π as 22/7 .)

Q:6 Shown below is a 5-minute sand timer. At the beginning, the sand has a height of 6 cm. After 5 minutes, the sand only occupies space in the cylindrical portion.

If the height of each conical section is h cm, then find the height of the sand in the bottom portion, after 5 minutes, in terms of h . Show your work. 

Q:7 Sudha's Printing Company has an order to print labels for flavoured yogurt cups for the brand Milky Waves, such that the label covers the entire curved surface of the cup. A picture of the cup is shown below.

Each of Sudha's rectangular printing sheets is 1 m long and 2 m wide and about 40% of each sheet is wasted due to the shape of the cup. 

Approximately how many labels can she print on one sheet? Show your work. 

(Note: Assume that each label covers the curved surface area of the cup without any overlap; the figure is not to scale; use π as 3.14.)

Q:8 A solid is made using a cylinder and a hemisphere. It is then dipped in red paint and cut vertically along the axis of symmetry as shown below. The unpainted surface of solid III is then painted yellow.

(Note: The figures are not to scale.) 

Find the surface area of solid III that is painted:

i) red.

ii) yellow. 

Show your work.

(Note: Take π as 22/7 .)

Q:9 A restaurant stores ice-cream in a box with a dispenser attached for filling ice-cream cones. The dimensions of the box and the ice-cream cones used by the restaurant are shown in Figure 1 below. To make each serving of dessert, the cone is first filled with ice-cream and then topped with a hemispherical scoop of ice-cream taken from the same box, as shown in Figure 2.

Approximately how many desserts can be served out of a completely filled box of ice-cream? Show your steps. 

(Note: Take π as 22/7 .)

Case Study

Answer the questions based on the given information. 

An indoor kids play area has a cuboidal sitting bench, a hopping ball and a play tent as shown in the figure. The hopping ball has a handle attached to a sphere. Air is filled in the spherical part which is locked using a peg. The tent consists of a conical section exactly on top of a cylindrical section. 

(Note: The figure is not to scale.) 

The height of the cylindrical section of the tent is one and a half times the height of the conical section of the tent. The height and the diameter of the conical section of the tent are equal. 

Q:10 Find the ratio of the volume of the cylindrical section to the volume of the conical section of the tent. Show your work.

Q:11 A kid pulls out the peg from the hopping ball. The ball starts to deflate such that the volume of the spherical part decreases at the rate of 18000 cm3 per minute. How long does it take to deflate the entire ball? Give your answer to the nearest minute. 

Q:12 The bench has a wooden frame consisting of four wooden planks. The thickness of each plank is 2 cm. The vertical wooden planks are fitted between the horizontal wooden planks.

If the weight of each wooden plank is 0.5 g per cm3 , what is the total weight of the wood in the frame? Show your work.