Question

a cylinder has a volume of 565.2 cm³ and a height of 10 cm. use the formula v = πr²h and 3.14 for π. what is the radius of the cylinder? round to the nearest hundredth. radius = cm

Explanation:

Step1: Substitute the given values into the formula

Given \( V = 565.2\space cm^{3}\), \( h = 10\space cm\), and \(\pi=3.14\). Substitute into \(V=\pi r^{2}h\):
\(565.2 = 3.14\times r^{2}\times10\)

Step2: Simplify the equation

First, calculate \(3.14\times10 = 31.4\). The equation becomes \(565.2=31.4r^{2}\).
Then, solve for \(r^{2}\) by dividing both sides by \(31.4\):
\(r^{2}=\frac{565.2}{31.4}\)
\(r^{2}=18\)

Step3: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is non - negative), \(r = \sqrt{18}\)
\(r=\sqrt{9\times2}=3\sqrt{2}\approx 4.24\)

Answer:

\(4.24\)