Problem Solving Algebra

Question

A cylinder has base radius 2x and height 3x.

A cone has base radius 3x and height h.

 

All measurements are in cm.

 

The volume of the cylinder and the volume of the cone are equal.

Find h in terms of x. Give your answer in its simplest form. Please help! :)

Answer 1

Volume of cone is  V = (1/3)πr²h

Volume of a cylinder is  V = πr²h

 

Set the volume of cone and volume of cylinder equal to each other.

 

(1/3)πr²h = πr²h

 

 

Now we substitute the given values for x.

 

(1/3)π(3x)²(h) = π(2x)²(3x)

 

3x²πh = 12x³π

 

 

Divide both sides of the equation by 3x²π.

 

h = 4x