Question

Sandra calculated the height of a cylinder that has a volume of 576 pi cubic centimeters and a radius of 8 centimeters. Her work is shown below. V = B h Step 1: 576 pi = pi 8 squared h Step 2: 576 pi = 64 pi h Step 3: StartFraction 576 pi Over 64 pi EndFraction = StartFraction 64 pi Over 64 pi EndFraction h Step 4: h = 9 pi cm What error did Sandra make when calculating the height of the cylinder? In step 1, she substituted into the volume formula incorrectly. In step 2, she calculated 8 squared incorrectly. It should be 16 rather than 64. In step 4, the pi should have canceled, making the correct answer 9 cm. Sandra calculated the height of the cylinder correctly.

Answer 1

Answer:

The error was made in step 4, $\pi$ should have also been cancelled making the correct answer as 9 cm.

Step-by-step explanation:

Given that:

Volume of cylinder, $V = 576 \pi\ cm^3$

Radius of cylinder, r = 8 cm

To find:

The error in calculating the height of cylinder by Sandra ?

Solution:

We know that volume of a cylinder is given as:

$V = B h$

Where B is the area of circular base and

h is the height of cylinder.

Area of a circle is given as, $B = \pi r^2$

Let us put it in the formula of volume:

$V = \pi r^2 h$

Step 1:

Putting the values of V and r:

$576\pi = \pi 8^2 h$

So, it is correct.

Step 2:

Solving square of 8:

$576\pi = \pi \times 64\times h$

So, step 2 is also correct.

Step 3:

$h=\dfrac{576\pi}{64 \pi} = \dfrac{64 \pi \times 9}{64\pi}$

Step 4:

Cancelling 64 $\times \pi$,

h = 9 cm

So, the error was made in step 4, $\pi$ should have also been cancelled making the correct answer as 9 cm.