Question

no additional details were added for this assignment. the volume of a cylinder is given by the formula ( v=pi r^{2} h ) where ( r ) is the radius of the base and ( h ) is the height of the cylinder. a storage silo shaped like a cylinder has an interior volume of 4,860 cubic meters. if its radius is 8.5 meters, what is the height of the silo? use ( pi = 3.14 ). round your answer to the nearest tenth at the end of the calculation. the height of the silo is meters.

Explanation:

Step1: Substitute the given values into the formula

Given \(V = 4860\), \(r = 8.5\), \(\pi=3.14\) into \(V=\pi r^{2}h\). First, calculate \(r^{2}=(8.5)^{2}=72.25\). Then the formula becomes \(4860 = 3.14\times72.25\times h\).

Step2: Simplify the right - hand side

Calculate \(3.14\times72.25 = 3.14\times(70 + 2.25)=3.14\times70+3.14\times2.25=219.8+7.065 = 226.865\). So the equation is \(4860=226.865h\).

Step3: Solve for \(h\)

Divide both sides of the equation by \(226.865\), \(h=\frac{4860}{226.865}\approx21.4\).

Answer:

\(21.4\)