If a diameter of a cylinder is 5 yd and the height is 8 yd what is the volume?

Step-by-step explanation:

The formula of a volume of a cylinder:

r - radius

H - height

We have the diameter d = 2r = 5yd → r = 2.5yd and the height H = 8yd.

Substitute:

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