Question

The picture shows 3 steel rods. The rods are congruent, solid cylinders. The area of the top of the one rod is 7.07 square centimeters. The area of the body of one rod is 39.58 square centimeters. Find the total surface area of the 3 rods.

a) 53.72
b) 46.65
c) 139.95
d) 161.16​

Answer 1

Answer: D, 161.16 square centimeters.

Explanation:

The surface area of a cylinder (shape of each steel rod) is given by this formula:

`A = 2\pi rh + 2\pi r^2`, where the first 2*pi*r*h measures the area of the curved surface while the second 2*pi*r^2 measures the area of the two circles on the top and bottom.

We are given the area of the top of one rod, which is 7.07 square centimeters.

We are also given the area of the body of one rod, which is 39.58 square centimeters.

The top of one rod is the shape of a circle, and we know there are two circles on both sides of a cylinder, so the surface area of both circular sides are 7.07.

The total surface area of a cylinder is the body plus both circular ends, so the surface area for this cylinder is:

39.58 + 7.07 + 7.07 = 53.72

There are three cylinders, so multiply this value by three to get the answer, 161.16 square centimeters.