Question

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)

Answer 1

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:

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

For Sphere

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\times3.14\times2.5^3=65.42in^3 \\ V=65.42in^3 \end{gathered}$

For Cylinder

$\begin{gathered} V=\pi r^2h \\ V=3.14\times2.5^2\times2.5=49.0625\approx49.06 \\ V=49.06in^3 \end{gathered}$

For Cone

$\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V=\frac{1}{3}\times2.5^2\times2.5=16.354\approx16.35 \\ V=16.35in^3 \end{gathered}$