Question

Four times the sum of the areas of the two circular faces of a cylinder is equal to the twice its curved surface area. The height of the cylinder is ________ the radius.

Answer 1

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

It is given that,

4 × Sum of areas of the two circular faces of the cylinder = 2 × Curved surface area of the cylinder

$\Rightarrow 4\times \left(\mathrm{\pi }{r}^2+\mathrm{\pi }{r}^2\right)=2\times 2\mathrm{\pi }rh$

$\Rightarrow 8\mathrm{\pi }{r}^2=4\mathrm{\pi }rh$

$\Rightarrow 2r=h$

Or h = 2r

Thus, the height of the cylinder is twice the radius of the cylinder.

Four times the sum of the areas of the two circular faces of a cylinder is equal to the twice its curved surface area. The height of the cylinder is __2 times__ the radius.