CBSE Class 10 Maths Chapter 13 Important Questions and Answers: Surface Areas and Volumes

CBSE Class 10 Maths Chapter 13 Important Questions and Answers: The important questions from Chapter 13 Surface Areas and Volumes of unit VI is given here along with the answers in the pdf attached towards the end.

CBSE Class 10 Maths Chapter 13 Important Questions and Answers: From Class 9^th itself, students have been made familiar with the characteristics of solids like cuboid, cone, cylinder, and sphere. They are also familiar on how to find their surface areas and volumes. In chapter 13 of Unit VI, Class 10 Mathematics, students are made familiar with the number of solids made up of combinations of two or more of the basic solids.

Chapter 13 covers topics such as Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

To check the syllabus topics in detail, visit CBSE Class 10 Maths Syllabus 2022-2023

 CBSE Class 10 Maths Chapter 13 Important Questions

MULTIPLE CHOICE QUESTIONS (1 MARK)

Q1. The ratio of the total surface area of a solid hemisphere to the square of its radius is

a) 2π : 1

b) 3 π: 1

c) 4 π : 1

d) 1: 4 π

Q2. The circumference of the edge of a hemispherical bowl is 132 cm. When π is taken as the capacity of the bowl in cm³ is :

a) 2772

b) 924

c) 19404

d) 9702

Q3. The radius of a wire is decreased to one third. If the volume remains the same, the length will become

a) 3 times

b) 6 times

c) 9 times

d) 27 times

Q4. The surface area of the two spheres are in the ratio 1 : 2. The ratio of their volumes is :

a) √2: 1

b) 1 : 2√2

c) 1 : 8

d) 1 : 4

Q5. The radius of a sphere is r cm. The sphere is divided into two equal parts. The whole surface area of two parts will be:

a) 8πr²

b) 6πr²

c) 4πr²

d) 3πr²

Q6. If the areas of three adjacent faces of a cuboid are X, Y and Z respectively, then the volume of cuboid is:

a) XYZ

b) 2XYZ

c) √XYZ

d) √2XYZ

Q7. Two cubes each of volume 8cm³ are joined end to end , then the surface area of the resulting cuboid is

a) 80 cm²

b) 64 cm²

c) 40 cm²

d) 8 cm²

Q8. If the radius of the base of a right circular cylinder is halved, keeping the height same, the ratio of the volume of the reduced cylinder to that of original cylinder is

a) 2 : 3

b) 3 : 4

c) 1 : 4

d) 4 : 1

Q9. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Ratio of their volumes is

a) 27 : 20

b) 20 : 27

c) 9: 4

d) 4 : 9

Q10.The ratio of the volumes of two spheres is 8 : 27 . If r and R are the radii of spheres respectively then (R – r) : r is :

a) 1 : 2

b) 1 : 3

c) 2 : 3

d) 4 : 9

OBJECTIVE TYPE QUESTIONS

Q1. The surface area of a sphere is the same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. Find the radius of the sphere.

Q2. Find the Total Surface Area of a hemispherical solid having radius 7 cm.

Q3. The volume of two cubes are in the ratio 8 : 64 , then find the ratio of their surface areas.

Q4. Find the volume of a right circular cylinder of base radius 7 cm and height 10 cm .

Q5. Find the curved surface area of a right circular cone of height 15 cm and base diameter 16 cm.

Q6. If h, c and V respectively are the height, curved surface area and volume of a cone then find 3πVh³ – c²h² + 9V² = ……………….

Q7. Find the volume of the greatest sphere that can be cut from a cylindrical log of wood of base radius 1 cm and height 5 cm.

Q8. A cone and a hemisphere have equal bases and equal volumes. What is the ratio of their heights?

Q9. How many bags of grain can be stored in a cubic granary 12m x 6m x 5m , if each bag occupies a space of 0.48 m³?

Q10. A cylinder and a cone are of same base radius and of same height. What is the ratio of their volumes?

SHORT ANSWER TYPE QUESTIONS – 2 MARKS

Q1. Two cubes each of volume 27cm³ are joined end to end to form a solid. Find the surface area of the solid.

Q2. Fifty circular plates each of radius 7cm and thickness 0.5cm are placed one above another to form a solid right circular cylinder. Find its TSA.

Q3. Two cubes of each side 4cm are joined end to end. Find the volume of the resulting solid.

Q4. A conical vessel whose inner radius is 10cm and height 48cm is full of water. Find the

volume of water in it.

Q5. Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9cm.

Q6. A circus tent is cylindrical up to a height of 3m and conical above it. If the diameter of the base is 105m and the slant height of the conical part is 53cm, find the total canvas required in making the tent.

SHORT ANSWER TYPE QUESTIONS – 3 MARKS

Q1. A toy is in the form of a cone mounted on a hemisphere of same radius 7 cm. If the total height of the toy is 31 cm, find its total surface area.

Q2. A rocket is in the form of a cylinder, closed at the lower end, has a cone attached to its top. If each one has a radius 20 cm and height 21 cm, find the surface area of the rocket.

Q3. An ice – cream cone consists of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5 cm and height of the ice – cream cone is 12.5 cm. Calculate the volume of

 the ice – cream in the cone.

Q4. A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the solid left out after the cone is carved out.

Q5. A semi-circular sheet of paper of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of the cup.

Q6. The largest possible cylinder is cut out from a wooden cube of edge 8 cm. Find the volume of wood remaining in the cube.

LONG ANSWER QUESTIONS ( 4 MARKS)

Q1. A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then find the ratio of the radius and the height of the conical part.

Q2. The sum of the radius of the base and height of a solid right circular cylinder is 37cm. if the total surface area of the solid cylinder is 1628 sq.cm, find the volume of the cylinder. (π= 22/7).

Q3. A hollow cylindrical pipe is made up of copper. It is 21 dm long. The outer and inner diameters of the pipe are 10cm and 6cm respectively. Find the volume of copper used in making the pipe (π= 22/7)

Q4. A metallic cylinder has radius 3cm and height 5cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole is drilled in the cylinder. The conical hole has a radius of 3/2 cm. and its depth is 8/9cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in the conical shape.

To check how well aligned your preparation is with the board’s model for the 2022-23 exam evaluation, check:

CBSE Class 10 Mathematics (Standard) Sample Paper 2023

CBSE Class 10 Mathematics (Basic) Sample Paper 2023

DOWNLOAD Answers to CBSE Class 10 Maths Chapter 12 Important Questions

Unit VI mensuration has another chapter in it. Chapter 12 Areas Related to Circles along with Chapter 13, carries 10 marks in total.  Candidates should make sure that they are well aware of the latest syllabus as many topics have been dropped off from the rationalized syllabus for CBSE Class 10 Mathematics 2022-23.

All the best!