The height of a right circular cylinder is twice the radius. Explain how to express the volume as a function of the radius.

The volume V of a right circular cylinder of height h and radius r is V = pir^2h. if the height is twice the radius, express the volume v as function r. Question 930208: the volume V of a right circular cylinder of height h and radius r is V = pir^2h

Step-by-step explanation:

Really hope that not  confusing

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4