help...Cylinders...?

Question

The total surface area in square meters of a cylinder with a 14 in height and a 12 in base is:

A. 240 pie
B. 156 pie
C. 312 pie
D. 204 pie

Answer 1

It's pi buddy, but anyway =p

height 14 in and I'm guessing 12 in base means the diameter is 12 inches which means radius is 6 inches.
So then SA = 2 * pi * r * h + 2 * pi * r^2
SA = 2pi * 6 * 14 + 2pi * 36
SA = 240 pi
A is the answer.

Answer 2

First, you need to find the surface area of the base of the cylinder, which is a circle. The area of a circle equals pi * (radius) ^ 2. You say the base is 12in, so the radius must be 6in. Then the surface area of the base is pi * 6 ^ 2 = 36pi. But there is also a top on the cylinder, which a circle with the same radius, so the surface area of the base and top together is 72pi. For the surface area of the body of the cylinder, if you imagine "unrolling" the cylinder, you will get a rectangle. Compute the area of the rectangle (length * width) and add to the area of the top and bottom together to get your total surface area of the cylinder. We know the width of the rectangle is 14in, but have to figure out the length. Again, we get this from the circular base, but from its circumference. The circumference of a circle equals pi * radius * 2. Our circle's circumference is then 2 * 6 * pi, or 12pi. Multiply by 14 to get 168pi. Add 72pi, and your result is 240pi, answer A.

Answer 3

Let
r = radius cylinder
h = height cylinder
S = surface area cylinder including its top and bottom

S = 2πr² + 2πrh = 2πr(r + h)

By base I assume you mean diameter. So the radius would be half that.

Now plug in the numbers.

S = 2πr(r + h) = 2π*(12/2)[(12/2) + 14] = 2π*6(6 + 14)

S = 12π(20) = 240π

The answer is A.