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]
