What is the surface area of a cylinder with a radius of 3 feet and a height of 4 feet?

To find the surface area of a cylinder, you can use the formula:

Surface Area = 2πr² + 2πrh

Where:

• r is the radius of the cylinder.
• h is the height of the cylinder.

In your case, the radius (r) is 3 feet and the height (h) is 4 feet.

Let’s break this down step by step:

1. Calculate the area of the top and bottom circles:
   A_circles = 2πr²
   A_circles = 2π(3)² = 2π(9) = 18π square feet
2. Calculate the area of the side (the curved surface):
   A_side = 2πrh
   A_side = 2π(3)(4) = 24π square feet

Now, we combine these two areas to find the total surface area:

Surface Area = 18π + 24π = 42π

To get a numerical value, we can use the approximation π ≈ 3.14:

Surface Area ≈ 42(3.14) ≈ 131.88 square feet

So, the total surface area of the cylinder is approximately 131.88 square feet.