Question

What is the diameter of a hemisphere that has a volume of 4,000pi cubic feet?

Answer 1

The volume of a hemisphere can be calculated usint the formula shown below:

`V=(2)/(3)\pi r^3`

Where "r" is the radius of the hemisphere.

According to the information given in the exercise, the jungle gym is a hemisphere and its volume is:

`V=4,000\pi\text{ }ft^3`

Then, you can substitute this value into the formula and solve for the radius "r":

`\begin{gathered} V=(2)/(3)\pi r^3 \\ \\ 4,000\pi\text{ }ft^3=(2)/(3)\pi r^3 \\ \\ \frac{(3)(4,000\pi\text{ }ft^(3))}{2\pi}=r^3 \\ \\ r=\sqrt[3]{\frac{(3)(4,000\pi\text{ }ft^(3))}{2\pi}} \end{gathered}`

Evaluating, you get:

`r=10\sqrt[3]{6}\text{ }ft`

By definition, the diameter is twice the radius, therefore, this is:

`\begin{gathered} d=(2)(10\sqrt[3]{6}\text{ }ft) \\ d=20\sqrt[3]{6}\text{ }ft \\ d\approx36.34\text{ }ft \end{gathered}`

The answer is:

`d\approx36.34\text{ }ft`