The volume of a cone with a height of 6 cm is 8 pi cubic centimeters. Which expression can be used to find r, the radius of the base of the cone?
6 = one-third pi (r squared) (8 pi)
8 pi = one-third pi (r) (6 squared)
6 = one-third (pi r)(8 pi)
8 pi = one-third pi (r squared) (6)
8 pi = one-third pi (r squared) (6)
To find the expression that can be used to find the radius of the base of the cone, we need to manipulate the given equation involving the volume of the cone.
The volume of a cone is given by the formula V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height.
Given that the volume of the cone is 8π cubic centimeters and the height is 6 cm, we can substitute these values into the formula:
8π = (1/3)πr^2(6)
Now, let's simplify this equation step-by-step to solve for r:
Step 1: Simplify the equation
8π = 2πr^2
Step 2: Divide both sides of the equation by 2π
4 = r^2
Step 3: Take the square root of both sides of the equation
√4 = √r^2
2 = r
Therefore, the expression that can be used to find the radius of the base of the cone is r = 2.