Question

find the height of a right circular cylinder whose radius is 4 inches and whose volume is 112π cubic inches. the volume of a right circular cylinder is given by the formula v = πr²h, where r is the radius and h is the height. h = \boxed{} inches

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a right circular cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 112\pi \) cubic inches and \( r = 4 \) inches. We need to solve for \( h \).

First, substitute the known values into the formula:
\( 112\pi = \pi (4)^2 h \)

Step2: Simplify the equation

Simplify the right - hand side. First, calculate \( (4)^2=16 \), so the equation becomes:
\( 112\pi=\pi\times16\times h \)

We can divide both sides of the equation by \( \pi \) (since \( \pi
eq0 \)) to get:
\( 112 = 16h \)

Step3: Solve for \( h \)

To solve for \( h \), divide both sides of the equation \( 112 = 16h \) by 16:
\( h=\frac{112}{16} \)
\( h = 7 \)

Answer:

7