Answer:
The volume of the cylinder is
[tex]V=99\ in^3[/tex]
Step-by-step explanation:
we know that
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
[tex]V=33\ in^3[/tex]
so
[tex]33=\frac{1}{3}\pi r^{2}h[/tex]
Multiply by 3 both sides
[tex]99=\pi r^{2}h[/tex] ----> equation A
Remember that
The volume of a cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
The cylinder has the same height and the same radius as the cone
so
Equate the volume of cylinder to equation A
[tex]V=99\ in^3[/tex]
The volume of the cylinder is 99 cubic inches and this can be determined by using the formula of the volume of the cylinder and the volume of the cone.
Given :
The formula of the volume of a cone is given by:
[tex]\rm V = \dfrac{1}{3}\pi r^2h[/tex]
[tex]\rm 3V = \pi r^2h[/tex] --- (1)
The formula of the volume of the cylinder is given by:
[tex]\rm V' = \pi (r')^2 h'[/tex] --- (2)
According to the given data, the cylinder has the same height and the same radius as the cone. That is:
h' = h
r' = r
So, from equations (1) and (2):
V' = 3V
According to the given data, V = 33 cubic inches.
V' = 3(33)
V' = 99 cubic inches
So, the volume of the cylinder is 99 cubic inches.
For more information, refer to the link given below:
https://brainly.com/question/23409099
