What is the radius of the cone?

Question

A cylinder and a cone have the same height and the same volume. The radius of a cylinder is 9 centimeters. What is the radius of the cone?

Answer 1

cylinder volume = cone volume

 

pi * r² * h = 1/3 pi * r² * h

 

9² = 1/3 * r²

 

r² = (3)*(9²)

 

r = 9*sqrt(3)

 

   = 15.588

 

 

Answer 2

Volume of a cylinder: V_cyl = πr²h

 

Volume of a cone: V_cone = 1/3 πr²h

 

Set both volumes equal, then put r = 9 cm in the cylinder volume. Solve for the remaining r:

 

π(9)²h = 1/3 πr²h

 

81 = 1/3 r²  (cancel π and h on both sides)

 

r² = 243

 

r = √243 = 9√3 ≈ 15.59 cm .

 

Now you have it exactly and rounded to two decimal places, as you need.