Question

a cylinder has a height of 8 inches. its volume is 1,607.68 cubic inches. what is the radius of the cylinder? use π ≈ 3.14 and round your answer to the nearest hundredth. r ≈ □ inches submit

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. We know \( V = 1607.68 \) cubic inches, \( h=8 \) inches, and \( \pi\approx3.14 \). We need to solve for \( r \).

First, substitute the known values into the formula:
\( 1607.68=3.14\times r^{2}\times8 \)

Step2: Simplify the right - hand side of the equation

Calculate \( 3.14\times8 = 25.12 \). So the equation becomes:
\( 1607.68 = 25.12r^{2} \)

Step3: Solve for \( r^{2} \)

Divide both sides of the equation by \( 25.12 \):
\( r^{2}=\frac{1607.68}{25.12} \)
\( r^{2}=64 \)

Step4: Solve for \( r \)

Take the square root of both sides. Since \( r \) represents the radius of a cylinder (a non - negative quantity), we consider the positive square root:
\( r=\sqrt{64} = 8.00 \) (rounded to the nearest hundredth)

Answer:

\( 8.00 \)