Question

The diameter of a rain barrel is 1. 2 meters and the surface area is 9. 0432 square meters. What is the height, in meters, of the barrel? Round your answer to the nearest tenth. Use 3. 14 for π

Answer 1

1.8 m

Explanation:

You want the height of a cylinder with diameter 1.2 m and total surface area of 9.0432 m².

Surface area

The area of a cylinder of radius r and height h is given by the formula ...

SA = 2πr(r +h)

Solving for h gives ...

r +h = SA/(2πr)

h = SA/(2πr) -r

Application

The radius is half the diameter, so is ...

r = d/2 = 1.2 m/2 = 0.6 m

Then the height is ...

h = 9.0432 m²/(2·3.14·0.6 m) -0.6 m

h = 1.8 m

The height of the barrel is about 1.8 meters.