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These two cylinders are congruent.

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?

Given:
[tex]\[ r = 4 \, \text{cm} \][/tex]
[tex]\[ V = 176\pi \, \text{cm}^3 \][/tex]

Find:
[tex]\[ h = \square \, \text{cm} \][/tex]

Sagot :

GinnyAnswer
To determine the height of Cylinder B, we start by using the given volume formula for a cylinder:

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

We know the following conditions for Cylinder B:
- The radius [tex]\( r \)[/tex] is 4 centimeters.
- The volume [tex]\( V \)[/tex] is [tex]\( 176 \pi \)[/tex] cubic centimeters.

We need to find the height [tex]\( h \)[/tex]. Let's substitute the known values into the volume formula and solve for [tex]\( h \)[/tex].

Given:
[tex]\[ V = 176 \pi \][/tex]
[tex]\[ r = 4 \, \text{cm} \][/tex]

Substitute [tex]\( r = 4 \)[/tex] into the volume formula:
[tex]\[ 176 \pi = \pi (4)^2 h \][/tex]

Simplify the equation:
[tex]\[ 176 \pi = \pi \cdot 16 \cdot h \][/tex]

Since π appears on both sides of the equation, we can cancel it out:
[tex]\[ 176 = 16h \][/tex]

Now, solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{176}{16} \][/tex]

Perform the division:
[tex]\[ h = 11 \][/tex]

Therefore, the height of Cylinder B is:
[tex]\[ h = 11 \, \text{cm} \][/tex]
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