## A cylinder and a cone have the same volume. The cylinder has radius x and height y . The cone has radius 3x . Find

Question

A cylinder and a cone have the same volume. The cylinder has radius x
and height y
. The cone has radius 3x
. Find the height of the cone in terms of y
.

in progress 0
1 week 2021-09-10T17:53:54+00:00 2 Answers 0

1. The height of the cone in terms of y would be

H=4y/3
SEE WORK BELOW:

V=∏x2y
cone
V=(1/3)∏(3x/2)2H where H=height of the cone
solve for H
set the volumes equal to each other
∏x2y=(1/3)∏(3x/2)2H
divide both sides by ∏
x2y=(1/3)(3x/2)2H
x2y=(1/3)(9×2/4)H
x2y=(3×2/4)H
x2y=(3/4)x2H
divide both sides by x2
y=(3/4)H
multiply both sides by (4/3)
(4/3)y=H
H=4y/3 or H=(4/3)y, either way, is the height of the cone

Step-by-step explanation:

The formula for calculating the volume of a cylinder is given as :

The formula for calculating the volume of a cone is given as :

Since the cylinder and the cone have the same volume according to the question , we will equate the two formulas, that is:

substituting the values of r , we have

since is common to both sides , it will cancel out , that is

divide through by 9

Therefore , the height of the cone in terms of y is