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?

Question

anonymous · Answer

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 · Answer

since half the diameter is the radius

anonymous · Answer

double that and you would have a diameter of 20  making the radius 10 
compute $$\pi\times 10^2\times 5$$

anonymous · Answer

we can do it without the numbers i chose if you like

anonymous · Answer

no i doubled the diameter from 10 to 20 so the radius got doubled from 5 to 10

anonymous · Answer

lets do it another way, without the made up numbers ok?

anonymous · Answer

Ok

anonymous · Answer

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 · Answer

so do I multiply $$125\pi \times4$$ ?

anonymous · Answer

yes

anonymous · Answer

which is the exact same thing you would get if you computed $$10^2\times 5\times \pi$$