Question

What is the radius of a hemisphere with a volume of 91358 in?, to thenearest tenth of an inch ? Help plssss

Answer 1

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:

`V_(HEMISPHERE)=(2)/(3)*\pi* r^3`

Step 2: Apply the formula to find the radius of the hemisphere in question, as follows:

`\begin{gathered} \text{Given that:} \\ V_(HEMISPHERE)=91,358in^3 \\ \text{and }\pi=3.142 \\ \text{Therefore:} \\ V_(HEMISPHERE)=(2)/(3)*\pi* r^3 \\ \Rightarrow91,358=(2)/(3)*3.142* r^3 \\ Multiply\text{ both sides of the equation by 3, thus:} \\ \Rightarrow91,358*3=2*3.142* r^3 \\ \text{Now:} \\ \Rightarrow2*3.142* r^3=91,358*3 \\ \Rightarrow r^3=(91,358*3)/(2*3.142) \\ \Rightarrow r^3=(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}`

Therefore, the radius of the hemisphere is 35.2 inches