Question

the volume of this cylinder is 3,014.4 cubic centimeters. what is the radius? round your answer to the nearest hundredth. 15 cm r ≈ centimeters submit

Explanation:

Step1: Write the volume formula for a cylinder

The volume formula for a cylinder is \( V=\pi r^{2}h \), where \( V = 3014.4\) \(cm^{3}\), \(h = 15\) \(cm\), and \(\pi\approx3.14\).

Step2: Substitute the known values into the formula

Substitute \(V = 3014.4\), \(h = 15\), and \(\pi=3.14\) into \(V=\pi r^{2}h\). We get \(3014.4 = 3.14\times r^{2}\times15\).
First, simplify the right - hand side: \(3.14\times15 = 47.1\). So the equation becomes \(3014.4=47.1r^{2}\).

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

Divide both sides of the equation \(3014.4 = 47.1r^{2}\) by \(47.1\).
\(r^{2}=\frac{3014.4}{47.1}\).
\(r^{2}=64\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r=\sqrt{64}\).
\(r = 8.00\) (exact value in this case, no need for further approximation as \(\sqrt{64}=8\))

Answer:

\(8.00\) centimeters