anonymous
  • anonymous
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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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
26π in3 16π in3 24π in3 32π in3
Valpey
  • Valpey
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
  • Valpey
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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anonymous
  • anonymous
oh ok
Valpey
  • Valpey
What is the volume of the cylinder in terms of \(\pi\)?
anonymous
  • anonymous
well pie is 3.14 right?
Valpey
  • Valpey
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
  • anonymous
oh ok well idk what the radius is but they tell us the height
Valpey
  • Valpey
The radius is half the diameter by definition.
anonymous
  • anonymous
oh ok so the radius would be 2?
Valpey
  • Valpey
Yes, the radius of the cylinder is 2.
anonymous
  • anonymous
ok so it would be π2^2*8
Valpey
  • Valpey
Yes, what is that equal to?
anonymous
  • anonymous
315.5072?
anonymous
  • anonymous
@Valpey
Valpey
  • Valpey
Not quite. Let's still leave it in terms of pi. Let's just resolve \(2^2 * 8\).
Valpey
  • Valpey
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
  • anonymous
oh ok 2^2*8 is 32
anonymous
  • anonymous
and yeah thats what i did

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