Question

A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 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(3in)2(12in) − 1.5(four over threeπ(9in)3)
π(12in)2(3in) − 1.5(four over threeπ(9in)3)
π(3in)2(12in) − 9(four over threeπ(1.5in)3)
π(12in)2(3in) − 9(four over threeπ(1.5in)3)

Answer 1

idk this im so sorry

Answer 2

Now, first off, you have to calculate the volume of the cilider defined by the water and sustract it the volume of each individual marble.
these are de equations you might want to use:
\[A _{Cil.}= h \pi r^2 \]
Where "h" is the height, and "r" the radius of the cilinder's base.
\[A _{sph.}=\frac{ 4 }{ 3 } \pi r^3\]
where "r" is the radius of the marble.

Answer 3

So, the volume of the water will be determined by the volume of the section it defines on the cilider sustracted by the volume of al lthe marbles:
\[Vol=h. \pi . r^2 - 9(\frac{ 4 }{ 3 } \pi r ^3 )\]

Answer 4

that eliminates a and c right?

Answer 5

is it D? @Owlcoffee

Answer 6

yes.

Answer 7

I don't know, you'll have to replace the values and see.

Answer 8

lol yeah thats what it matches

Answer 9

Yes, then "D" is the correct option.