Question

Find the height of a right cylinder with surface area 160pie square units and radius 5 units

Answer 1

Given:

Radius of a cylinder = 5 units.

Surface area of the cylinder = $160\pi$

To find:

The height of the right cylinder.

Solution:

Surface area of a cylinder is:

$A=2\pi rh+2\pi r^2$

Where, r is radius and h is the height of the cylinder.

Putting $r=5, A=160\pi$ in the above formula, we get

$160\pi =2\pi (5)(h)+2\pi (5)^2$

$160\pi =10\pi h+2\pi (25)$

$160\pi =10\pi h+50\pi$

Subtract $50\pi$ from both sides.

$160\pi -50\pi=10\pi h$

$110\pi=10\pi h$

Divide both sides by $10\pi$.

$\dfrac{110\pi}{10\pi}=h$

$11=h$

Therefore, the height of the cylinder is 11 units.