Question

The radius of a sphere is 10 inches. a) What is the volume, in cubic inches, of the sphere?The height is the volume, h, the cylinder is 2 times the radius.b) What is the volume of the cylinder?

Answer 1

`\begin{gathered} \text{ The volume of the sphere is calculated using the formula} \\ V_{\text{sphere}}=(4)/(3)\pi r^2 \\ \text{ since }r=10inches \\ V_{\text{sphere}}=(4)/(3)\pi r^3 \\ V_{\text{sphere}}=(4)/(3)(3.14159)(10)^3 \\ V_{\text{sphere}}=(4)/(3)(3.14159)(1000)^{}=4188.8\text{ inches\textasciicircum{}3} \\ \text{ The volume of the sphere 4188.8 cubic inches} \end{gathered}`
`\begin{gathered} \text{ Since the height of the cylinder is 2 times the radius,} \\ \text{given that radius is 10 inches, the height is 20 inches} \\ \text{ The volume of the cylinder is calculated using the formula} \\ V_{\text{cylinder}}=\pi r^2h \\ \text{ Substitute the following values and we have} \\ V_{\text{cylinder}}=\pi r^2h \\ V_{\text{cylinder}}=(3.14159)(10)^2(20) \\ V_{\text{cylinder}}=(3.14159)(100)^{}(20)=6283.2\text{ cubic inches} \end{gathered}`