Question

(A)Which figures have a volume greater than 600 cubic inches (b)How many times greater is the volume of the sphere than the volume of cone 1. Round your answer to the nearest tenth. "

Answer 1

Answer:

(A)Cylinder 2 and the sphere

(B)4.8

Explanation:

$\begin{gathered} \text{Volume of a cylinder =}\pi r^2h \\ \text{Volume of a cone=}\frac{1}{3}\pi r^2h \\ \text{Volume of a sphere=}\frac{4}{3}\pi r^3 \end{gathered}$

Cylinder 1

$\begin{gathered} \text{Volume}=\pi\times6^2\times5 \\ \approx565\text{ cubic inches} \end{gathered}$

Cylinder 2

$\begin{gathered} \text{Volume}=\pi\times6^2\times15 \\ \approx1696\text{ cubic inches} \end{gathered}$

Cone 1

$\begin{gathered} \text{Volume}=\frac{1}{3}\times\pi\times6^2\times5 \\ \approx188\text{ cubic inches} \end{gathered}$

Cone 2

$\begin{gathered} \text{Volume}=\frac{1}{3}\times\pi\times6^2\times15 \\ \approx565\text{ cubic inches} \end{gathered}$

Sphere

$\begin{gathered} \text{Volume}=\frac{4}{3}\times\pi\times6^3 \\ \approx905\text{ cubic inches} \end{gathered}$

Therefore: Cylinder 2 and the sphere have a volume greater than 600 cubic inches ​.

Part B

$\begin{gathered} \text{Difference}=\frac{Volume\text{ of sphere}}{\text{Volume of cone 1}} \\ =(\frac{4}{3}\times\pi\times6^3)\div(\frac{1}{3}\times\pi\times6^2\times5) \\ =288\pi\div60\pi \\ =4.8 \end{gathered}$

The volume of the sphere is 4.8 times greater than the volume of cone 1.