Question

A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 7 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches.

Which of the following could be used to calculate the volume of water in the vase?

π(12in)2(3in) − 7(four over threeπ(1.5in)3)
π(3in)2(12in) − 7(four over threeπ(1.5in)3)
π(12in)2(3in) − 1.5(four over threeπ(7in)3)
π(3in)2(12in) − 1.5(four over threeπ(7in)3)

Answer 1

@snowflake0531

Answer 2

\[V = 2\pi r(h)\]
And so we want to subtract the volume of where there's no water from teh volume of the whole vase

Answer 3

Wrote wrong, you have to subtract those weird marbles oops <.<

Answer 4

So we have the sphere volume as \[\frac{ 4 }{ 3 } \pi r^3\] and we have 7 of those so \[7(\frac{ 4 }{ 3 } \pi r^3)\]

Answer 5

So that is what we have to subtract

Answer 6

So we have to find the volume of hte whole cylinder, and subtract and 7 spheres

Answer 7

\[\pi r^2(h) - 7(\frac{ 4 }{ 3 } \pi r^3)\]

Answer 8

So now we put the h and r values in
For the first one
Height: 12 inches, diameter is 6, which means that radius is 3

\[\pi(3^2)(12)-7(\frac{ 4 }{ 3 }\pi r^3)\]

Answer 9

Then for the second one, we have diameter of 3, radius of 1.5
\[\pi(3^2)(12)-7(\frac{ 4 }{ 3 }\pi 1.5^3)\]

Answer 10

So, I think you got the answer now

Ithink the choices were copied and pasted weirdly