Question

Billy’s exercise ball contains 0.523 m3 of air. What is the radius of the exercise ball? Use 3.14 for π and round your answer to the nearest tenth of a meter.

Answer 1

The radius of exercise ball is 0.5 meter, if Billy’s exercise ball contains 0.523
`m^(3)` of air and
`\pi` = 3.14.

Explanation:

The given is,

Volume of exercise ball = 0.523 cubic meter

Step:1

Exercise ball looks like a sphere,

Formula foe volume of sphere,

`Volume, V = (4)/(3) \pi r^(3)`......................(1)

Where, r - Radius of sphere

From given, V = 0.523 cubic meters

Equation (1) becomes,

`0.523 = (4)/(3) \pi r^(3)`

`0.523 = (4)/(3) (3.14) r^(3)` (∵
`\pi` = 3.14 )

`0.523 = (1.333)(3.14)r^(3)`

`0.523 = (4.18667)r^(3)`

`r^(3) = (0.523)/(4.18667)`

`r^(3) = 0.12492`

Take cube root on both sides,

`r=\sqrt[3]{0.12492}`

r = 0.49989

r ≅ 0.5 meter

Result:

The radius of exercise ball is 0.5 meter, if Billy’s exercise ball contains 0.523
`m^(3)` of air and
`\pi` = 3.14.