Question

A cylinder is labeled with a height of 8 yards and a radius of 7 yards.

Find the surface area of the cylinder. Use the approximation of 3.14 for pi.

Answer 1

[AI-generated answer — Explain Bot]

To find the surface area of a cylinder, you need to compute the sum of the areas of its two circular bases and its curved surface.

First, let's find the area of the circular bases. The formula to calculate the area of a circle is A = π * r^2, where A is the area and r is the radius.

Given that the radius of the cylinder is 7 yards, we can find the area of each circular base:

Base Area = π * (7)^2
Base Area = 3.14 * (7)^2
Base Area ≈ 3.14 * 49
Base Area ≈ 153.86 square yards

Since there are two bases, we will multiply this area by 2.

Total Base Area = 2 * 153.86 square yards
Total Base Area ≈ 307.72 square yards

Next, let's calculate the curved surface area of the cylinder. The formula for the curved surface area of a cylinder is A = 2πrh, where A is the area, r is the radius, and h is the height of the cylinder.

Given that the radius of the cylinder is 7 yards and the height is 8 yards, we can find the curved surface area:

Curved Surface Area = 2 * 3.14 * 7 * 8
Curved Surface Area ≈ 351.68 square yards

Finally, we calculate the total surface area by adding the areas of the two circular bases and the curved surface:

Total Surface Area = Total Base Area + Curved Surface Area
Total Surface Area ≈ 307.72 + 351.68
Total Surface Area ≈ 659.40 square yards

So, the approximate surface area of the cylinder is 659.40 square yards.