Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750π. What is the percent change in volume between cylinders A and B?

Question

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

what's the volume of cylinder A?

anonymous · Answer

1570.796

whpalmer4 · Answer

keep it symbolic, that will make your life much easier

anonymous · Answer

what do you mean

whpalmer4 · Answer

instead of multiplying by 3.1415926535..., just write down the symbol for pi

anonymous · Answer

thats what i did

whpalmer4 · Answer

do the final arithmetic when the problem is done

so the volume of cylinder A is 500 pi

anonymous · Answer

ok so what come next

whpalmer4 · Answer

what is the percentage change between 500 pi and 750 pi?  hint: it's the same as the percentage change between 500 and 750, or 50 and 75, or 10 and 15

whpalmer4 · Answer

but if you had 1570.8 and 2356.19, it wouldn't be nearly so obvious that they had pi as a common factor, right?

anonymous · Answer

these are the answer  choices 

Cylinder B is 50% smaller than cylinder A.

 Cylinder B is 75% smaller than cylinder A.

 Cylinder B is 50% bigger than cylinder A.

 Cylinder B is 200% bigger than cylinder A.

whpalmer4 · Answer

okay, so, cylinder A is 500 pi units, and cylinder B is 750 pi units.  is B larger or smaller than A?

anonymous · Answer

larger

whpalmer4 · Answer

okay, so that eliminates half the answers right there :-)

to find the percentage change between A and B, calculate

(B - A)/B  * 100%

anonymous · Answer

would it be  Cylinder B is 50% bigger than cylinder A.

whpalmer4 · Answer

sorry 

(B-A)/A * 100% if going from A to B

whpalmer4 · Answer

(750 pi - 500 pi)/(500 pi) * 100% = 250/500 * 100% = 50%, yes.

anonymous · Answer

ok thanks

whpalmer4 · Answer

when we kept the manipulation symbolic (didn't turn pi into a number), it was much easier
and we didn't have to worry about any rounding errors or the like.