Question

Sandra calculated the height of a cylinder that has a volume of 576(pie) cubic centimeters and a radius of 8 centimeters. Her work is shown below.

V=Bh
Step 1: 576(pie)= (pie)8^2h
Step 2: 576(pie) = 64(pie)h
Step 3: 576(pie)/64(pie) = 64(pie)/64(pie)h
Step 4: h=9(pie) cm

What error did Sandra make when calculating the height of the cylinder?
A. In step 1, she substituted into the volume formula incorrectly.
B. In step 2, she calculated 8^2 incorrectly. It should be 16 rather than 64.
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
D. Sandra calculated the height of the cylinder correctly.

Answer 1

See below.

Explanation:

Step 3 should be: 576pi / 64pi = 64pi h / 64pi

Step 4: 9 = h.

I would say C and D.

Answer 2

C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.

Explanation:

We know that,

The volume of a cylinder is,

`V=\pi(r)^2h`

Where r is the radius of the cylinder,

h be the height of the cylinder,

Given,

`V=576\pi \text{ cubic cm}`

r = 8 cm,

So, for finding the height of the cylinder the steps are as follows,

Step 1 :
`576\pi =\pi (8)^2h`

Step 2 :
`576\pi =\pi (64)h`

Step 3 :
`(576\pi)/(64\pi) =(\pi (64))/(64\pi)h`

Step 4 :
`h = 9\text{ cm}`

Thus, it is clear that she had her mistake in 4th step,

She should cancel out
`\pi`.

Option C is correct.