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Cylinder A has a radius of 4 centimeters. Cylinder B has a volume of [tex]$176 \pi$[/tex] cubic centimeters. What is the height of Cylinder B?

[tex]h = \square[/tex] cm

Answer :

To find the height of Cylinder B, we start with the formula for the volume of a cylinder:

[tex]$$
V = \pi r^2 h
$$[/tex]

We are given that Cylinder B has a volume of

[tex]$$
V = 176\pi \quad \text{cm}^3,
$$[/tex]

and we assume its radius is the same as Cylinder A, which is

[tex]$$
r = 4 \quad \text{cm}.
$$[/tex]

First, we calculate the area of the base of the cylinder:

[tex]$$
\text{Base Area} = \pi r^2 = \pi (4)^2 = 16\pi.
$$[/tex]

Next, we solve for the height [tex]$h$[/tex] by rearranging the volume formula:

[tex]$$
h = \frac{V}{\pi r^2}.
$$[/tex]

Substitute the given values into the equation:

[tex]$$
h = \frac{176\pi}{16\pi}.
$$[/tex]

Since [tex]$\pi$[/tex] cancels out in the numerator and denominator, we have:

[tex]$$
h = \frac{176}{16}.
$$[/tex]

Dividing [tex]$176$[/tex] by [tex]$16$[/tex] gives:

[tex]$$
h = 11.
$$[/tex]

Thus, the height of Cylinder B is

[tex]$$
\boxed{11} \quad \text{cm}.
$$[/tex]

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