Question

The radius of the base of a cylinder is increased from 4 cm to 16 cm, but its curved surface area remains unchanged. If the initial height of the cylinder was 4 cm, what will be its new height?

• A. 2 cm
• B. 4 cm
• C. 3 cm
• D. 1 cm

Answer 1

Answer:

D. 1 cm

Solution:

Given: 

Initial radius (r) = 4 cm 

New radius (R) = 16 cm

Initial height (h) = 4 cm

New height = H cm

Both curved surface area of the cylinder remains unchanged.

Formula Used:

Curved Surface Area of cylinder = 2πrh

Where, r = Radius of cylinder

h = Height of cylinder

Calculation:

Initial curved surface area = 2 × π × 4 × 4 

= 32π cm²

New curved surface area = 2 × π × 16 × H 

= 32πH cm²

As, Initial curved surface area = New curved surface area

⇒ 32π = 32πH

⇒ H = 1 cm

Hence, the new height of the cylinder is 1 cm.