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?

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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?

Mathematics
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26π in3 16π in3 24π in3 32π in3
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.
The volume of a cylinder is \(\pi r^2 h\) (r, the radius is half the diameter) The volume of a sphere is \(\frac{4}{3}\pi r^3\)

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oh ok
What is the volume of the cylinder in terms of \(\pi\)?
well pie is 3.14 right?
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 \(y = \frac{2}{3}\pi\).
oh ok well idk what the radius is but they tell us the height
The radius is half the diameter by definition.
oh ok so the radius would be 2?
Yes, the radius of the cylinder is 2.
ok so it would be π2^2*8
Yes, what is that equal to?
315.5072?
Not quite. Let's still leave it in terms of pi. Let's just resolve \(2^2 * 8\).
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.
oh ok 2^2*8 is 32
and yeah thats what i did

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