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Sagot :
First, we have to find the volume of each figure.
Sphere.
[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\cdot\pi(r)^3=\frac{4}{3}\cdot3.14\cdot(6)^3 \\ V_{\text{sphere}}=904.32in^3_{} \end{gathered}[/tex]Cylinder #1.
[tex]\begin{gathered} V_1=\pi(r)^2h=3.14\cdot(6)^2\cdot5 \\ V_1=565.2in^3 \end{gathered}[/tex]Cylinder #2.
[tex]\begin{gathered} C_2=\pi(r)^2h=3.14\cdot6^2\cdot15 \\ C=1695.6in^3 \end{gathered}[/tex]Cone #1.
[tex]\begin{gathered} V_{\text{cone}1}=\frac{1}{3}\pi(r)^2h=\frac{1}{3}\cdot3.14\cdot6^2\cdot5 \\ V_{\text{cone}1}=188.4in^3 \end{gathered}[/tex]Cone #2.
[tex]\begin{gathered} V_{\text{cone}2}=\frac{1}{3}\pi(r)^2h=\frac{_{}1}{3}\cdot3.14\cdot6^2\cdot15 \\ V_{\text{cone}2}=565.2in^3 \end{gathered}[/tex]Part A: So, according to these volumes, the sphere and Cylinder 2 are the only figures with a volume greater than 600 cubic inches.
Part B.
Let's divide the volume of the sphere by the volume of Cone #1.
[tex]\frac{904.32}{188.4}=4.8[/tex]Hence, the volume of the sphere is 4.8 times greater than the volume of Cone #1.
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