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

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).

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