Answer:
r = 3 in; h = 6 in
Step-by-step explanation:
Since diameter = twice radius, d = 2r. Here the diameter equals the height. Therefore, 2r = h.
The formula for the volume of a cylinder is V = πr²h. We will substitute 2r for h, obtaining: V = πr²·2r = 2πr³.
We are told that the volume is 54π in³. We equate this to the formula 2πr³:
54π in³ = 2πr³.
Dividing both sides by 2π yields:
27 in³ = r³
Taking the cube root of both sides yields r = 3 in.
The radius of the cup is 3 in, the diameter is 2(3 in) = 6 in, and the height of the cup is 6 in (since the height and diameter are the same).
