Cylinder, Cone and Sphere

Appeared in 10 of the 11 available papers.

Examined in

10 of 11 papers

Appears almost every year — treat as core

Typically worth

7.1 marks

Average per paper it appears in · 71 marks in total

Usual form

Numerical

81% of this chapter's 31 questions

Needs a diagram

61%

19 questions carry a figure — practise drawing them

Question-type distribution

Numerical25
MCQ6

Most frequent topics

Mensuration of solids 19Mensuration 10Circle theorems 2

Print:Questions only Questions + answers Answers only

Print chapter question bank

Showing 25 of 31 matching questions (71 marks).

25 questions

1

Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.)

1(vii)2026

MCQEasy1 mark

The total surface area of a solid sphere (S1) and a solid hemisphere (S2), as shown in the diagram, are equal. The ratio of radii R and r is :

(a)1 : 1
(b)2 : 1
(c)√3 : 2
(d)2 : √3

Diagram for question 1(vii)

3(ii)

An eye drop bottle is prepared consisting of a hemisphere, a cylinder and a conical cap, as shown in the given diagram. Height of the cylindrical and conical parts are each, equal to the diameter (7 cm). Find the :

Figure for this question

3(ii)(a)2026

NumericalModerate2 marks

minimum height of the cylindrical box required to pack this bottle.

3(ii)(b)2026

NumericalModerate2 marks

volume of the liquid medicine (shaded part) in the bottle. Give your answer to the nearest whole number. (Use π = 22/7 )

9(iii)

A solid wooden toy is prepared by joining a cone, a cylinder and a sphere, as shown in the given diagram. The radius of each of the three solids is 7 cm and heights of each of the cone and the cylinder is 24 cm. Find :

Figure for this question

9(iii)(a)2026

NumericalModerate2 marks

the total surface area of the given solid.

9(iii)(b)2026

NumericalModerate2 marks

the cost of painting the total surface at the rate of ₹0.50 per cm.

1

Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.)

1(xii)2025

MCQEasy1 mark

If the volume of two spheres is in the ratio 27: 64, then the ratio of their radii is:

(a)3 : 4
(b)4 : 3
(c)9 : 16
(d)16 : 9

5(iii)2025

NumericalHard4 marks

A solid wooden capsule is shown in Figure 1. The capsule is formed of a cylindrical block and two hemispheres. Find the sum of total surface area of the three parts as shown in Figure 2. Given, the radius of the capsule is 3.5 cm and the length of the cylindrical block is 14 cm. (Use π = 22/7 )

Diagram for question 5(iii)

9(i)2025

NumericalModerate3 marks

A hollow sphere of external diameter 10 cm and internal diameter 6 cm is melted and made into a solid right circular cone of height 8 cm. Find the radius of the cone so formed. (Use π = 22/7)

Diagram for question 9(i)

1

Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.)

1(xiv)2024

MCQEasy1 mark

Question 1(xiv): A rectangular sheet of paper of size 11 cm × 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is:

(a)1 : 1
(b)7 : 11
(c)11 : 7
(d)11π/7 : 7π/11

Diagram for question 1(xiv)

2(ii)

A solid metallic cylinder is cut into two identical halves along its height. The diameter of the cylinder is 7 cm and the height is 10 cm. Find :

Figure for this question

2(ii)(a)2024

NumericalModerate2 marks

The total surface area (both the halves).

2(ii)(b)2024

NumericalModerate2 marks

Calculate the total cost of painting the two halves at the rate of ₹ 30 per cm². (use π = 22/7)

8(iii)2024

NumericalModerate3 marks

Oil is stored in a spherical vessel occupying 3/4 of its full capacity. Radius of this spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with a radius of 21 cm. Find the height of the oil in the cylindrical vessel (correct to the nearest cm). Take π = 22/7

Diagram for question 8(iii)

1

Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.)

1(xiii)2023

MCQEasy1 mark

Volume of a cylinder of height 3 cm is 48π. Radius of the cylinder is :

(a)48 cm
(b)16 cm
(c)4 cm
(d)24 cm

7(iii)2023

NumericalHard4 marks

A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height so that the solid is completely submerged in water. If the radius of the cylinder is 14 cm, find the rise in the water level.

Diagram for question 7(iii)

1

Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.)

1(ii)2022

MCQEasy1 mark

The volume of a conical tent is 462 m³ and the area of the base is 154 m². The height of the cone is:

(a)15 m
(b)12 m
(c)9 m
(d)24 m

1(x)2022

MCQEasy1 mark

The radius of a roller 100 cm long is 14 cm. The curved surface area of the roller is (Take π = 22/7):

(a)13200 cm²
(b)15400 cm²
(c)4400 cm²
(d)8800 cm²

3(ii)2022

NumericalModerate2 marks

A solid cone of radius 5 cm and height 9 cm is melted and made into small cylinders of radius of 0.5 cm and height 1.5 cm. Find the number of cylinders so formed.

4(iv)2022

NumericalModerate3 marks

A solid wooden cylinder is of radius 6 cm and height 16 cm. Two cones each of radius 2 cm and height 6 cm are drilled out of the cylinder. Find the volume of the remaining solid.

Diagram for question 4(iv)

4(a)2020

NumericalModerate3 marks

A solid spherical ball of radius 6 cm is melted and recast into 64 identical spherical marbles. Find the radius of each marble.

11(b)2020

NumericalModerate3 marks

From a solid wooden cylinder of height 28 cm and diameter 6 cm, two conical cavities are hollowed out. The diameters of the cones are also of 6 cm and height 10.5 cm. Taking π = 22/7 find the volume of the remaining solid.

Diagram for question 11(b)

3(c)

A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the:

3(c)(i)2019

NumericalModerate2 marks

radius of the cylinder.

3(c)(ii)2019

NumericalModerate2 marks

curved surface area of the cylinder. [Take π = 3.1]

6

Figure for this question

6(c)2019

NumericalHard4 marks

A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows: The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm. Give your answer correct to the nearest whole number. Take π=22 7 .

2(a)

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the

2(a)(i)2018

NumericalModerate1.5 marks

radius of the cylinder

2(a)(ii)2018

NumericalModerate1.5 marks

volume of cylinder. (use π = 22/7 )