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

Question

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## Answers ( )

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

Answer: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⇒sinceis common to both sides , it will cancel out , that isdivide through by 9

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