Question

Question 4
If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

Answer 1

True.
Let the radius of a cylinder be r and height be h.

Curved surface area of a cylinder $=2\pi rh$

Let the new radius, $r_1=2r$ and height be H.

Curved surface of the cylinder is not changed; therefore,

$2\pi rh=2\pi \left(2r\right)\times H$

$\Rightarrow 2\pi rh=4\pi rH$

$\Rightarrow H=\frac{2\pi rh}{4\pi r}\Rightarrow H=\frac{h}{2}$

Hence, the height must be halved.