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.
