A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 6 centimeters. Find the radius.

Question

 I need help on this because standardized testing is comeing up and I dont understand how to do this

 

Answer 1

First set the volumes equal to each other, knowing the formulas.

 

(4/3)πr³ = πr²h

 

 

Then plug in the height if cylinder, which is h=6.

 

(4/3)πr³ = 6πr²

 

 

Now you can solve for r from this equation.

 

Multiply both sides of the equation by 3/4.

 

πr³ = (9/2)πr²

 

 

Move all terms to the left side of the equation.

 

πr³ - 4.5πr² = 0

 

Factor out πr².

 

πr²(r - 4.5) = 0

 

 

Since r cannot be zero, the radius is then 4.5 cm.