Question

A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 marbles, each of diameter 2 inches. The vase is filled with water up to a height of 12 inches.

What is the volume of water in the vase?

96π in3

27π in3

65π in3

105π in3

Answer 1

calculate the volume of the marbles (V = 4/3 π r^3), then multiply that by nine.
calculate the volume of the vase (V = π r^2 h), then subtract the marbles' volume.

Answer 2

π(3^2)(12)??

Answer 3

but aren't there only 9 marbles? You put 12.

Answer 4

12=h

Answer 5

marble volume

\[V = 9 \times \frac{4}{3} \pi \times1^3\]

\[V = 12 \pi\]

volume of the vase

\[V = \pi \times 3^2 \times 12\]

\[V = 108 \pi\]

Volume of water

\[V = 108 \pi - 12 \pi = 96 \pi\]

Answer 6

thank you both:)

Answer 7

calculate volume of each marble and then total volume occupied by the marbles. now, actual volume of water = volume of water column (i.e. up to the ht of water level) - total volume occupied by the marbles

Answer 8

thanks @annas

Answer 9

my pleasure :)

Answer 10

is the answer 96 pie