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- yeval76

Cylinder A has a radius of 12 inches and a height of 6 inches. Cylinder B has a volume of 648π. What is the percent change in volume between cylinders A and B?
Cylinder B is 50% smaller than cylinder A.
Cylinder B is 25% smaller than cylinder A.
Cylinder B is 150% bigger than cylinder A.
Cylinder B is 200% bigger than cylinder A.

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- yeval76

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- yeval76

- yeval76

- mathstudent55

First, find the volume of cylinder A.

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- mathstudent55

Do you know how to find the volume of a cylinder?

- yeval76

The volume of cylinder A is 2,712.96

- mathstudent55

\(\Large V_{cylinder} = \pi r^2 h\)
where r = radius of the base, and
h = height of the cuylinder

- yeval76

Yea so the volume of cylinder A is 2,712.96

- yeval76

So what do I do now?

- mathstudent55

Correct.
Since the volume of cylinder B is written in terms of pi, you can also write the volume of cylinder A in terms of pi. (In other words, don't multiply pi in the formula.)
\(\Large V_{A} = 864 \pi\)
\(\Large V_B = 648 \pi\)
Ok so far?

- yeval76

Yes mam or sir

- yeval76

Would you divide Va by Vb and then multiply it by 100...

- mathstudent55

Now we need the second step of the problem. We need to find the percent change. Look in all choices. Every choice states "Cylinder B is ... than cylinder A."
This means we are comparing cylinder B to A.

- mathstudent55

Here is the formula to calculate percent change:
\(percent~change = \dfrac{new~amount - old~amount}{old~amount} \times 100\)
If the percent change is positive, it is an increase. If the percent change is negative, it is a decrease.
In this case, since we are comparing cylinder B to cylinder A, then
old amount = 864 pi
new amount = 648 pi
(pi will cancel out in the calculation.)

- yeval76

So will it be 25% smaller then cylinder A right?

- mathstudent55

Correct.

- yeval76

Yayyyy Thank You!!! @mathstudent55

- mathstudent55

You're welcome.

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