Question

A cylinder shaped storage tank has a radius of (x+5) metres and a height of x metres. Determine the dimensions (round to two decimal places) of the tank if the volume is about 192 cubic metres.

Answer 1

Radius = 6.46 meters

Height = 1.46 meters

Explanation:

The volume of a cylinder = πr²h

In the above question, we were given

r = (x + 5) meters

h = x meters

Volume = 192 cubic meters

Hence,

192 = π × (x + 5)² × x

192 = π × (x² + 10x + 25) × x

192 = π × (x³ + 10x² + 25x)

Divide both sides by π

192/π = x³ + 10x² + 25x

61.115498147 = x³ + 10x² + 25x

x³ + 10x² + 25x - 61.12

This Quadratic equation is a polynomial

x = 1.46119

From the above:

Radius = (x + 5)meters

Radius = 1.46119 + 5 = 6.46119 meters

Approximately to 2 decimal places = 6.46 meters

Height = x meters

Height = 1.46119 meters

Approximately to 2 decimal places = 1.46 meters