Question

these two cylinders are congruent.
cylinder a
( r = 4 ) cm
cylinder b
( v = 176pi ) ( \text{cm}^3 )
cylinder a has a radius of 4 centimeters. cylinder b has a volume of ( 176pi ) cubic centimeters. what is the height of cylinder b?
( h = square ) cm

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Since the two cylinders are congruent, Cylinder B has the same radius as Cylinder A, so \( r = 4 \) cm for Cylinder B.

Step2: Substitute the known values into the volume formula

We know that \( V = 176\pi \) and \( r = 4 \). Substituting these into the formula \( V = \pi r^2 h \), we get:
\[
176\pi = \pi (4)^2 h
\]

Step3: Simplify and solve for \( h \)

First, simplify \( (4)^2 = 16 \), so the equation becomes:
\[
176\pi = \pi \times 16 \times h
\]
We can divide both sides of the equation by \( \pi \) to cancel out \( \pi \) from both sides:
\[
176 = 16h
\]
Then, divide both sides by 16 to solve for \( h \):
\[
h = \frac{176}{16} = 11
\]

Answer:

11