Answer:
[tex]30cm^3[/tex]
Step-by-step explanation:
the volume of a cylinder is given by:
[tex]v_{cylinder}=\pi r^2 h[/tex]
and the volume of a cone is given by:
[tex]v_{cone}=\frac{\pi r^2 h}{3}[/tex]
since both have the same height and radius, we can solve each equation for [tex]r^2h[/tex] (because this quantity is the same in both figures) and then match the expressions we find:
from the cylinder's volume formula:
[tex]r^2h=\frac{v_{cylinder}}{\pi}[/tex]
and from the cone's volume formula:
[tex]r^2h=\frac{3 v_{cone}}{\pi}[/tex]
matching the two previous expressions:
[tex]\frac{v_{cylinder}}{\pi} =\frac{3v_{cone}}{\pi}[/tex]
we solve for the volume of a cone [tex]v_{cone}[/tex]:
[tex]v_{cone}=\frac{\pi v_{cylinder}}{3\pi} \\\\v_{cone}=\frac{v_{cylinder}}{3}[/tex]
substituting the value of the cylinder's volume [tex]v_{cylinder}=90cm^3[/tex]
[tex]v_{cone}=\frac{90cm^3}{3} \\\\v_{cone}=30cm^3[/tex]
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 = [tex]\frac{1}{3}[/tex] 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 = [tex]\frac{1}{3}[/tex] πr² h
= [tex]\frac{1}{3}[/tex] (volume of a cylinder)
from the question given, volume of the cylinder = 90 cm³
volume of a cone = [tex]\frac{1}{3}[/tex] (volume of a cylinder)
=[tex]\frac{1}{3}[/tex] × 90
= 30 cm³
Therefore, volume of the cone = 30 cm³
