Question

I need help with this problem

Answer 1

`22.2 \;meters`

Explanation:

The volume of the hemisphere = 22,778 m³

The volume of a sphere of the same radius
= twice the volume of the hemisphere
= 2 x 22,778 m³
= 45576 m³

The volume of a sphere of radius r is given by the formula:

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

Plugging in knowns:

`45576 =(4)/(3)\pi r^3`

Switching sides:

`(4)/(3)\pi r^3 =45576`

Multiply both sides by
`(3)/(4)`

`(3)/(4) * (4)/(3)\pi r^3 =(3)/(4) * 45576\\\\\pi r^3 = 34,182`

Divide by π both sides to get

`r^3 = (34,182)/(\pi) = 10,880.4685\\\\r= \sqrt[3]{10,880.4685} \\\\= 22.15895\\\\= 22. 2 \text{ meters (to the nearest tenth)}`