The volume of a right circular cone is exactly . If the altitude of the cone has a length of 12 feet, what is the length of radius of the circular base?
A)4 ft
B)4.25 ft
C)4.5 ft
D)4.75 ft

Question

The volume of a right circular cone is exactly  . If the altitude of the cone has a length of 12 feet, what is the length of radius of the circular base?
A)4 ft 
B)4.25 ft 
C)4.5 ft 
D)4.75 ft

Quizplus · Accepted Answer

The volume of a right circular cone is given by the formula V = (1/3)πr^2h, where r is the radius of the circular base and h is the altitude (height) of the cone.
Substituting the given values, we get:
11ebfb55_24c3_6835_9d86_bdb0da7efdd9_TBX8811_11 = (1/3)πr^2(12)
Multiplying both sides by 3 and dividing by π and 12, we get:
r^2 = 11ebfb55_24c3_6835_9d86_bdb0da7efdd9_TBX8811_11 / (4π)
Taking the square root, we get:
r = √(11ebfb55_24c3_6835_9d86_bdb0da7efdd9_TBX8811_11 / (4π))
Using a calculator, we get:
r ≈ 4.5 ft
Therefore, the length of the radius of the circular base is 4.5 feet. The correct answer is (C).

The Volume of a Right Circular Cone Is Exactly