What is the surface area of a right cylinder which has a base with radius 9 units and has a height of 12 units?

C

Step-by-step explanation:

The formula for surface area of a cylinder is A=2πrh+2πr². Since we know the radius and height, we can directly plug it into this formula to find surface area.

A=2π(9)(12)+2π(9²)

A=2π(108)+2π(81)

A=216π+162π

A=378π

A=1186.92 units²

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

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