Acylinder has a radius of 3 cm and a height of 24 cm. what is the area of the rectangle made by the circumference and height of this cylinder?

a) 508.68 cm2

b) 480.42 cm2

c) 452.16 cm2

d) 84.78 cm2

Option C.

Step-by-step explanation:

step 1

Find the circumference

The circumference of a circle is equal to

we have

substitute

step 2

Find the area of the rectangle made by the circumference and height of the cylinder

The area of the rectangle is equal to

substitute the values

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64

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