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?

Correct option is B

Given:

Radius of base of cylinder increased form 4cm to 16cm

Curved surface area remains unchanged

Initial height of cykinder is 4cm

Formula Used:

Curved surface area of cylinder $$= 2 \pi r h$$​​

Solution:

Curved surface area initiallly when r =  4cm and  height = 4cm

​$$= 2 \pi (4)(4)$$​​

​$$= 32\pi cm^2$$​​

If radius is increased to 16cm then let new height be $$h_1$$​​

So curved surface area = $$2 \pi (16)(h_1) = 32\pi h_1$$​​

But area remains unchanged hence

​$$32\pi h_1 = 32 \pi$$​​

​$$h_1 = 1cm$$​​