Question

Part AWhich figures have a volume greater than 600 cubic inches?A Cylinder #1BCone #1c Cylinder #2D Cone #2E Sphere(b)Part BHow many times greater is the volume of the Sphere than the volume of Cone#1? Round your answer to the nearest tenth.Enter your answer in the boxHi

Answer 1

(a)C and E

(b)4.8 times

Step-by-step explanation:

Part A

First, calculate the volumes of all the given solids:

Cylinder 1

`\begin{gathered} V=\pi r^2h=\pi*6^2*5=180\pi \\ \approx565\; in^3 \end{gathered}`

Cylinder 2

`\begin{gathered} V=\pi r^2h=\pi*6^2*15=540\pi \\ \approx1696\; in^3 \end{gathered}`

Cone 1

`\begin{gathered} V=(1)/(3)\pi r^2h=(1)/(3)*\pi*6^2*5=60\pi \\ \approx188\; in^3 \end{gathered}`

Cone 2

`\begin{gathered} V=(1)/(3)\pi r^2h=(1)/(3)*\pi*6^2*15=180\pi \\ \approx565\; in^3 \end{gathered}`

Sphere

`\begin{gathered} V=(4)/(3)\pi r^3=(4)/(3)*\pi*6^3=288\pi \\ \approx905\; in^3 \end{gathered}`

The figures that have a volume greater than 600 cubic inches are:

• C Cylinder #2

,

• E Sphere

Part B

`\begin{gathered} \frac{\text{Volume of Sphere}}{\text{Volume of Cone 1}}=(288\pi)/(60\pi) \\ =4.8 \end{gathered}`

The volume of the sphere is 4.8 times the volume of Cone 1.