Question

the volume of this cylinder is 5,652 cubic yards. what is the radius? use π ≈ 3.14 and round your answer to the nearest hundredth. 8 yd r ≈ □ yards 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 that \( V = 5652 \) cubic yards, \( h=8 \) yards, and \( \pi\approx3.14 \). We need to solve for \( r \).

First, substitute the known values into the formula:
\( 5652=3.14\times r^{2}\times8 \)

Step2: Simplify the right - hand side of the equation

Calculate \( 3.14\times8 \):
\( 3.14\times8 = 25.12 \)
So the equation becomes \( 5652 = 25.12r^{2} \)

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

Divide both sides of the equation by \( 25.12 \):
\( r^{2}=\frac{5652}{25.12} \)
\( \frac{5652}{25.12}=225 \) (since \( 25.12\times225 = 25.12\times(200 + 25)=25.12\times200+25.12\times25 = 5024+628 = 5652 \))
So \( r^{2}=225 \)

Step4: Solve for \( r \)

Take the square root of both sides. Since \( r \) represents the radius (a non - negative quantity), we have:
\( r=\sqrt{225}=15.00 \) (rounded to the nearest hundredth)

Answer:

\( 15.00 \)