Question

the volume of this cylinder is 14,736.02 cubic millimeters. what is the height? round your answer to the nearest hundredth. 19 mm h h ≈ millimeters submit

Explanation:

Step1: Calculate the base area

The formula for the area of a circle (base of the cylinder) is \(A = \pi r^{2}\). Given \(r = 19\) mm, then \(A=\pi\times(19)^{2}=\pi\times361\approx3.14\times361 = 1131.54\) \(mm^{2}\).

Step2: Find the height

The volume formula of a cylinder is \(V=Ah\) (where \(V\) is volume, \(A\) is base - area, \(h\) is height). We know \(V = 14736.02\) \(mm^{3}\) and \(A\approx1131.54\) \(mm^{2}\). Rearranging for \(h\), we get \(h=\frac{V}{A}\). Substitute \(V\) and \(A\) values: \(h=\frac{14736.02}{1131.54}\approx13.02\)

Answer:

\(13.02\)