CBSE Class 9 Mathematics Surface Areas And Volumes Worksheet Set B

CBSE Class 9 Mathematics Worksheet - Surface areas and Volumes - Practice worksheets for CBSE students. Prepared by teachers of the best CBSE schools in India.

Case study question- 1

An antique box and its dimensions excluding the stand is given below.

Question. What is the volume of the jewellery box?
a) (𝑙×𝑏×ℎ) + 𝜋𝑟²ℎ
b) (𝑙×𝑏×ℎ) + 1/2 𝜋𝑟²ℎ
c) 2(𝑙𝑏×𝑏ℎ × 𝑙ℎ)+𝜋𝑟²ℎ
d) (𝑙×𝑏×ℎ) + 2𝜋𝑟ℎ
Answer : B

Question. How much brass will be needed to plate the curved surface of the dome as shown in figure?
a) 1320cm²
b) 220 cm²
c) 440 cm²
d) 660 cm²
Answer : D

Question. How many sheets of dimensions 14cm x 30cm x 2cm can be placed in the box?
a) 10
b) 5
c) 2
d) 15
Answer : B

Question. Considering the thickness of the box to be negligible, how much velvet cloth will be needed to cover the cuboidal inner area?
a) 1720 cm²
b) 880 cm²
c) 1300 cm²
d) 1580 cm²
Answer : C

Very Short Answer type Questions

Question. 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.
Answer : 9735m²

Question. A bird-bath in a garden is in the shape of a cylinder with a hemi-spherical depression at one end. The height of the hollow cylinder is 1.45m and its radius is 30cm. find the TSA of the bird-bath.
Answer : 3.3m²

Question. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder
Answer : 4620 cm³

Question. Two cubes each of side 4cm are joined end to end. Find the volume of the resulting solid.
Answer : 128cm³

Question. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
Answer : 9units

Question. 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.
Answer : 133: 2

Question. A rectangular sheet of paper 30cm x 18cm can be transformed into the curved surface of a right circular cylinder in two ways either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volume of the two cylinders thus formed.
Answer : 5:3

Question. Find the volume of a right circular cylinder of base radius 7 cm and height 10 cm.
Answer : 1540 cm³

Question. A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the ratio between the radius of their bases to their heights is 3:4
Answer : 3:4

Question. The internal and external diameters of a hollow hemispherical vessel are 12cm and 16cm respectively. If the cost of painting 1 sq.cm of the surface area is Rs. 5, find the total cost of painting the vessel all over. (π = 3.14)
Answer : Rs. 3579.60

Question. 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)
Answer : 4620 cub.cm

Question. 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.
Answer : 205.33 cm³

Question. From a solid cylinder of height 14 cm and base radius 7 cm, two identical conical holes from each end of radius 2.1 cm and height 4 cm are drilled out. Find the volume of the remaining solid.
Answer : 2119.04 cm³

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 9 Mathematics Worksheet - Surface areas and Volumes