Question

A sphere and a cylinder each have the same radius. The cylinder has a height that is triple the radius. Which figure has a greater volume, the cylinder or the sphere?

Answer 1

we calculate the volume of the two solids

Sphere

$V_s=\frac{4}{3}\times\pi\times r^3$

Cylinder

$\begin{gathered} V_c=\pi\times r^2\times h \\ V_c=\pi\times r^2\times3r \\ V_c=\pi\times3r^3 \end{gathered}$$\begin{gathered} \frac{4}{3}\times\pi\times r^3 \\ \\ 3\times\pi\times r^3 \end{gathered}$

the comparison allows us to see that the volume of the cylinder is greater than that of the sphere