Question a-righ
A right circular cone has a volume of 
cubic feet and a height of 9 feet. What is the radius, in feet, of the base of the cone?
3
A right circular cone has a volume of cubic feet and a height of 9 feet.
Hard-difficulty · SAT Math · Area and Volume — Volume of prisms, cylinders, cones, spheres. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice A is correct. The equation for the volume of a right circular cone is 
. It’s given that the volume of the right circular cone is cubic feet and the height is 9 feet. Substituting these values for V and h, respectively, gives 
. Dividing both sides of the equation by gives 
. Dividing both sides of the equation by 9 gives 
. Taking the square root of both sides results in two possible values for the radius, 
or 
. Since the radius can’t have a negative value, that leaves as the only possibility. Applying the quotient property of square roots, 
, results in 
, or 
.
Choices B and C are incorrect and may result from incorrectly evaluating . Choice D is incorrect and may result from solving 
instead of 
.
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