The height and diameter of a cylindrical cup are the same length. The volume of the cup is 54pi in3 what is the radius and the height of the cup
r = 3 in; h = 6 in
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).
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Mathematics, published 11.05.2023
Mathematics, published 23.03.2023