It takes a pump 3 hours to fill a cylindrical barrel. How long would it take the pump to fill a barrel with the same height but twice the radius? Please show the work.

Question

anonymous · Answer

bet it would be 4 times as long. lets check

anonymous · Answer

the answer is we hours so you are right
i jsut want to see the work

anonymous · Answer

since you know neither height nor radius it doesn't matter so we can make up numbers. suppose the radius of the first barrel is 1 and the height is h.  then the volume is 
$$\pi r^2h = \pi h$$ now if the radius doubles to be 2, then the volume is 
$$ \pi \times 2^2 \times h = 4\pi h$$ so the volume is increased by a factor of 4

anonymous · Answer

thank you !

anonymous · Answer

therefore it will take 4 times as long

anonymous · Answer

yw