Question

a cone and a cylinder have the same base radius and the same height if the volume of the cone is 10n cubic units what is the volume of the cylinder?

Answer 1

To find the volume of a cylinder with the same base radius \( r \) and height \( h \) as a cone, we can use the formulas for their volumes.

The volume \( V \) of a cone is given by:
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]

The volume \( V \) of a cylinder is given by:
\[
V_{\text{cylinder}} = \pi r^2 h
\]

According to the problem, the volume of the cone is \( 10n \) cubic units, so we can set up the equation:
\[
\frac{1}{3} \pi r^2 h = 10n
\]

To find the volume of the cylinder, we start with the formula for the volume of the cylinder:
\[
V_{\text{cylinder}} = \pi r^2 h
\]

Now, from the volume of the cone equation, we can express \( \pi r^2 h \) in terms of \( 10n \):
\[
\pi r^2 h = 3 \times 10n = 30n
\]

Thus, the volume of the cylinder is:
\[
V_{\text{cylinder}} = 30n
\]

So, the volume of the cylinder is \( \boxed{30n} \) cubic units.