Respuesta :
To obtain the value of the radius of the hemisphere, the following steps are necessary:
Step 1: Recall the formula for the volume of a hemisphere, as follows:
[tex]V_{HEMISPHERE}=\frac{2}{3}\times\pi\times r^3[/tex]Step 2: Apply the formula to find the radius of the hemisphere in question, as follows:
[tex]\begin{gathered} \text{Given that:} \\ V_{HEMISPHERE}=91,358in^3 \\ \text{and }\pi=3.142 \\ \text{Therefore:} \\ V_{HEMISPHERE}=\frac{2}{3}\times\pi\times r^3 \\ \Rightarrow91,358=\frac{2}{3}\times3.142\times r^3 \\ Multiply\text{ both sides of the equation by 3, thus:} \\ \Rightarrow91,358\times3=2\times3.142\times r^3 \\ \text{Now:} \\ \Rightarrow2\times3.142\times r^3=91,358\times3 \\ \Rightarrow r^3=\frac{91,358\times3}{2\times3.142} \\ \Rightarrow r^3=\frac{274074}{6.284}=43,614.577 \\ \Rightarrow r^3=43,614.577 \\ \Rightarrow r=\sqrt[3]{43,614.577}=35.20 \\ \Rightarrow r=35.2in\text{ (to the nearest tenth of an inch)} \end{gathered}[/tex]Therefore, the radius of the hemisphere is 35.2 inches
