anonymous
  • anonymous
A pool is shaped like a cylinder, and has a volume of 125(pi) cubic feet. What is the volume of another pool has the same height but doubled diameter?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
say the height is 5 and the diameter is 10, the the volume would be \(\pi\times r^2h=\pi \times 5^2\times 5=125\pi\)
anonymous
  • anonymous
since half the diameter is the radius
anonymous
  • anonymous
double that and you would have a diameter of 20 making the radius 10 compute \[\pi\times 10^2\times 5\]

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anonymous
  • anonymous
we can do it without the numbers i chose if you like
anonymous
  • anonymous
no i doubled the diameter from 10 to 20 so the radius got doubled from 5 to 10
anonymous
  • anonymous
lets do it another way, without the made up numbers ok?
anonymous
  • anonymous
Ok
anonymous
  • anonymous
when you compute the volume it is the area of the circle times the height the area goes with the square, as in \(A=\pi r^2\) therefore, if you double the diameter i.e. multiply it by 2 the area of the circle is multiplied by \(2^2=4\) in other words the area will be 4 times as large making the volume also 4 times as large (since the height is fixed)
anonymous
  • anonymous
so do I multiply \[125\pi \times4\] ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
which is the exact same thing you would get if you computed \[10^2\times 5\times \pi\]

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