1 Answer

WayneOS · Answer 1 · 2024-01-02T19:15:20+0000

First, we have to find the volume of each figure.

Sphere.

$\begin{gathered} V_{\text{sphere}}=(4)/(3)\cdot\pi(r)^3=(4)/(3)\cdot3.14\cdot(6)^3 \\ V_{\text{sphere}}=904.32in^3_{} \end{gathered}$

$\begin{gathered} V_1=\pi(r)^2h=3.14\cdot(6)^2\cdot5 \\ V_1=565.2in^3 \end{gathered}$

$\begin{gathered} C_2=\pi(r)^2h=3.14\cdot6^2\cdot15 \\ C=1695.6in^3 \end{gathered}$

$\begin{gathered} V_{\text{cone}1}=(1)/(3)\pi(r)^2h=(1)/(3)\cdot3.14\cdot6^2\cdot5 \\ V_{\text{cone}1}=188.4in^3 \end{gathered}$

$\begin{gathered} V_{\text{cone}2}=(1)/(3)\pi(r)^2h=\frac{_{}1}{3}\cdot3.14\cdot6^2\cdot15 \\ V_{\text{cone}2}=565.2in^3 \end{gathered}$

Let's divide the volume of the sphere by the volume of Cone #1.

Hence, the volume of the sphere is 4.8 times greater than the volume of Cone #1.