Question

The surface area of a cylinder is 432 pi yd2. The height of the cylinder is five times the radius. What is the diameter of the cylinder?

Answer 1

Since the surface area of this cylinder is $432\pi \;yd^2$, its diameter is equal to 12 yards.

How to calculate surface area.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

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

Where:

• h is the height.

• r is the radius.

Given the following data:

• Surface area of cylinder = $432\pi \;yd^2$

• Height = 5r.

Substituting the given parameters into the formula, we have;

$432\pi = 2\pi r(5r) + 2\pi r^2\\\\432\pi = 2\pi 5r^2 + 2\pi r^2\\\\216=5r^2+r^2\\\\216=6r^2\\\\r^2=36\\\\r=\sqrt{36}$

r = 6 yards.

For the diameter:

Diamter = 2 x radius

Diamter = 2 x 6

Diameter = 12 yards.

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