A cylindrical vase has a diameter of 4 inches. At the bottom of the vase, there are 6 marbles, each of diameter 2 inch. The vase is filled with water up to a height of 8 inches. What is the volume of water in the vase?

Question

anonymous · Answer

26π in3
 16π in3 
24π in3 
32π in3

valpey · Answer

You need to solve for the total volume of the cylinder, then subtract the total volume of the marbles to get the total volume of the water.

valpey · Answer

The volume of a cylinder is $\pi r^2 h$ (r, the radius is half the diameter)
The volume of a sphere is $\frac{4}{3}\pi r^3$

anonymous · Answer

oh ok

valpey · Answer

What is the volume of the cylinder in terms of $\pi$?

anonymous · Answer

well pie is 3.14 right?

valpey · Answer

It isn't necessary to use the numerical value of pi. You can leave everything in terms of pi. As in $x = 15\pi$ or $y = \frac{2}{3}\pi$.

anonymous · Answer

oh ok well idk what the radius is but they tell us the height

valpey · Answer

The radius is half the diameter by definition.

anonymous · Answer

oh ok so the radius would be 2?

valpey · Answer

Yes, the radius of the cylinder is 2.

anonymous · Answer

ok so it would be π2^2*8

valpey · Answer

Yes, what is that equal to?

anonymous · Answer

315.5072?

anonymous · Answer

@Valpey

valpey · Answer

Not quite. Let's still leave it in terms of pi. Let's just resolve $2^2 * 8$.

valpey · Answer

I think you did $(\pi*2)^2 * 8$ when you meant to do $\pi*(2)^2 * 8$. Still, we don't actually need to multiply by pi.

anonymous · Answer

oh ok 2^2*8 is 32

anonymous · Answer

and yeah thats what i did