The volume of a hemisphere can be calculated usint the formula shown below:
[tex]V=\frac{2}{3}\pi r^3[/tex]
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:
[tex]V=4,000\pi\text{ }ft^3[/tex]
Then, you can substitute this value into the formula and solve for the radius "r":
[tex]\begin{gathered} V=\frac{2}{3}\pi r^3 \\ \\ 4,000\pi\text{ }ft^3=\frac{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}[/tex]
Evaluating, you get:
[tex]r=10\sqrt[3]{6}\text{ }ft[/tex]
By definition, the diameter is twice the radius, therefore, this is:
[tex]\begin{gathered} d=(2)(10\sqrt[3]{6}\text{ }ft) \\ d=20\sqrt[3]{6}\text{ }ft \\ d\approx36.34\text{ }ft \end{gathered}[/tex]
The answer is:
[tex]d\approx36.34\text{ }ft[/tex]
