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frank has a cylinder cup that has a radius of 3 inches and a height of 6 inches. it holds 58 marbles. leah has a different cylinder cup that has a radius of 5 inches and a height of 8 inches. how many marbles would her cup hold?



Answer :

MathPhys

Answer:

214

Step-by-step explanation:

Ignoring any differences in the packing of the marbles, the number of marbles is proportional to the volume of the cylinder cup. The volume of a cylinder is equal to pi times the square of the radius times the height.

The volume of Frank's cylinder is:

V = πr²h

V = π (3 in)² (6 in)

V = 54π in³

The volume of Leah's cylinder is:

V = πr²h

V = π (5 in)² (8 in)

V = 200π in³

Writing a proportion:

58 / 54π = x / 200π

x = 214.8

Rounding down to the nearest marble, Leah's cup can hold 214 marbles.

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