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the cylinder cone and sphere each share the same radius and height the sphere has a diameter of 5 in. find the radius height in the volume for all three objects(round volume to the nearest hundredth)

the cylinder cone and sphere each share the same radius and height the sphere has-example-1
User Fpes
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1 Answer

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Let's begin by listing out the information given to us

The height & radius is the same for all the figures

Diameter (D) = 5 in; radius (r) = D/2 = 5/2 = 2.5 in

Height (h) = 2.5 in

The volume of the shapes are given below:


\begin{gathered} Cylinder\colon V=\pi r^2h \\ Cone\colon V=(1)/(3)\pi r^2h \\ Sphere\colon V=(4)/(3)\pi r^3 \\ \\ \end{gathered}

For Sphere


\begin{gathered} V=(4)/(3)\pi r^3 \\ V=(4)/(3)*3.14*2.5^3=65.42in^3 \\ V=65.42in^3 \end{gathered}

For Cylinder


\begin{gathered} V=\pi r^2h \\ V=3.14*2.5^2*2.5=49.0625\approx49.06 \\ V=49.06in^3 \end{gathered}

For Cone


\begin{gathered} V=(1)/(3)\pi r^2h \\ V=(1)/(3)*2.5^2*2.5=16.354\approx16.35 \\ V=16.35in^3 \end{gathered}

User Antonio
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