Question

CASE STUDY: To make the teaching, learning process easier, creative, and

innovative, A teacher brings clay in the classroom to teach the topic mensuration.

She thought this method of teaching is more interesting, leave a long-lasting

impact She forms a cylinder of radius 6 cm and height 8 cm with the clay, then she

moulds the cylinder into a sphere and asks some question to students [use π =

3.14]

i. The radius of the sphere so formed is:

a. 6 cm b. 7 cm c. 4 cm d. 8 cm

ii. The volume of the sphere so formed is :

a. 902.32 cm3 b. 899.34 cm3 c. 904.32 cm3 d. 999.33 cm3

iii. What is the ratio of the volume of a sphere to the volume of a cylinder?

a. 1:2 b. 2:1 c. 1:1 d. 3:1

iv. During the conversion of a solid from one shape to another the volume of the

new shape will:

a. increase b. decrease c. remain unaltered d. be double​

Answer 1

Answer:

i. (d) 8 cm

ii. (c) 904.32

iii. (c) 1:1

iv. (c) remain unaltered

Answer 2

Given:

Radius of the cylinder = 6 cm

Height of the cylinder = 8 cm

To find:

i. The radius of the sphere so formed.

ii. The volume of the sphere so formed.

iii. What is the ratio of the volume of a sphere to the volume of a cylinder?

iv. During the conversion of a solid from one shape to another the volume of the new shape will

Solution:

The volume of the cylinder will be

Volume = $\pi r^{2}h$

Volume = 3.14 x 36 x 8 = 904.32 $cm^3$

i. The radius of the sphere so formed.

To find the radius of the sphere so formed we will equate the volumes of sphere and cylinder.

The volume of sphere = $\frac{4}{3} \pi r^{3}$ = volume of cylinder

$\frac{4}{3} \pi r^{3}$  = 904.32

$r^3$ = 216

r = 6cm

Therefore the radius of the sphere so formed will be 6 cm (option a).

ii. The volume of the sphere so formed.

The volume of the sphere so formed will be equal to the volume of the cylinder which is 904.32 $cm^3$ (option c).

iii. What is the ratio of the volume of a sphere to the volume of a cylinder?

As the volume of the cylinder is equal to the volume of the sphere, therefore the ratio of their volumes will be 1:1 (option c).

iv. During the conversion of a solid from one shape to another the volume of the new shape will remain unaltered.