Question

A cone and a cylinder have the same height and their bases are congruent circles

Answer 1

Answer:

$30cm^3$

Step-by-step explanation:

the volume of a cylinder is given by:

$v_{cylinder}=\pi r^2 h$

and the volume of a cone is given by:

$v_{cone}=\frac{\pi r^2 h}{3}$

since both have the same height and radius, we can solve each equation for $r^2h$ (because this quantity is the same in both figures) and then match the expressions we find:

from the cylinder's volume formula:

$r^2h=\frac{v_{cylinder}}{\pi}$

and from the cone's volume formula:

$r^2h=\frac{3 v_{cone}}{\pi}$

matching the two previous expressions:

$\frac{v_{cylinder}}{\pi} =\frac{3v_{cone}}{\pi}$

we solve for the volume of a cone $v_{cone}$:

$v_{cone}=\frac{\pi v_{cylinder}}{3\pi} \\\\v_{cone}=\frac{v_{cylinder}}{3}$

substituting the value of the cylinder's volume $v_{cylinder}=90cm^3$

$v_{cone}=\frac{90cm^3}{3} \\\\v_{cone}=30cm^3$

Answer 2

Answer:

volume of the cone = 30 cm³

Step-by-step explanation:

first write both the formula for  finding the volume a cone and a cylinder

volume of a cone = $\frac{1}{3}$ πr² h

where r is the radius of the cone and h is the height of the cone

volume of a cylinder = πr²h

where r is the radius of the cylinder  and h is the height of a cylinder

since the cone and the cylinder has the same height and they are congruent which implies they have the same radius, then

volume of  a cone =   $\frac{1}{3}$ πr² h

                               = $\frac{1}{3}$ (volume of a cylinder)

                         

   from the question given, volume of the cylinder = 90 cm³

volume of a cone = $\frac{1}{3}$ (volume of a cylinder)

                              =$\frac{1}{3}$ × 90

                               = 30 cm³

Therefore, volume of the cone = 30 cm³