What is the surface area of this cylinder? show steps!

area = (exact) 88pi ft^2 or (approximate) 276 ft^2

Step-by-step explanation:

The surface area of a cylinder is the sum of the areas of the bases, two circles, and the lateral area which is a rectangle.

Each base is a circle, and the two bases are congruent, so find the area of one base and multiply by 2.

The lateral area is a rectangle. You need to find the length and width of the rectangle. Think of a can of food with a label wrapped around. If you make a vertical cut from one base to the other, and you unwrap the label, you will see that the lateral surface of a cylinder is a rectangle that has the height of the cylinder as its length, and the circumference of the base are its width.

area of circle = pi *r^2

area of rectangle = length * width

length of rectangle: length = 2(pi)r

width of rectangle: width = height = h

total area of cylinder = area of bases + lateral area

total area of cylinder = 2 * pi *r^2 + 2(pi)r * h

total area of cylinder = 2 * pi * (2 ft)^2 + 2 * pi * 2 ft * 20 ft

total area of cylinder = 8pi ft^2 + 80pi ft^2

total area of cylinder = 88pi ft^2

The exact area is 88pi ft^2.

If you need an approximate area, then use 3.14 for pi.

area = 88 * 3.14 ft^2

area = 276 ft^2

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