Answer:
The surface area of the cylinder is approximately 1256.6 square feet.
Step-by-step explanation:
The surface area of a cylinder can be separated into the area of two identical circles and a rectangle with bends along the circumference of the circles.
Let's start with the circle bases. The formula for the area of a circle is πr², and we are given the radius' measurement of 10 ft. Put that into our formula:
[tex]\pi 10^{2}[/tex] = [tex]100\pi[/tex]
There are two circles, so:
[tex]100\pi *2=200\pi[/tex]
We will keep our values in terms of pi as long as we can in order to keep our answers as accurate as we can until we must round.
We know that one side of the rectangle is 10 feet, but the sides next to that 10 feet are wrapped around the circles. We have to find the circumference of one of the circles to find the other side of the rectangle.
The formula for the circumference of a circle is 2πr, so we will plug our 10 ft radius into our formula.
[tex]2\pi (10) = 20\pi[/tex]
Now we can use our two side lengths 10 and 20π, to find the area of the rectangle.
A = [tex]10 * 20\pi = 200\pi[/tex]
Now we have the area of the two circle bases, 200π, and the area of the rectangle, 200π. Add these to find the total surface area.
200π + 200π = 400π ≈ 1256.637
The surface area of the cylinder is approximately 1256.6 square feet.
