What is the surface area of this cylinder? The radius is 12 yd and the height is 6 yd Surface area = Atop + Abottom + Aside Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. Find the radius and height of the cylinder. The circle on the bottom of the cylinder is the same, so: Find the circumference of the top circle. Now find the area of the curved surface. The curved surface is a rectangle. One side length is the height, and the other side length is the circumference of the circle. Now add the areas to find the surface area of the cylinder. The surface area of the cylinder is about _____ square yards

Answer 1

To find the surface area of the cylinder, we can break it down into its components:

1. Area of the top circle (Atop): \[ Atop = \pi r^2 \] where \( r = 12 \) yd.

   \[ Atop = 3.14 \times (12)^2 = 3.14 \times 144 = 452.16 \text{ square yards} \]

2. Area of the bottom circle (Abottom): Since the bottom circle has the same radius as the top circle: \[ Abottom = Atop = 452.16 \text{ square yards} \]

3. Area of the curved surface (Aside): To find the curved surface area, we first calculate the circumference of the circle (which is one side of the rectangle): \[ \text{Circumference} = 2\pi r = 2 \times 3.14 \times 12 = 75.36 \text{ yards} \] The curved surface area is the circumference times the height: \[ Aside = \text{Circumference} \times \text{Height} = 75.36 \times 6 = 452.16 \text{ square yards} \]

4. Total Surface Area: Now, add all these areas together: \[ \text{Surface Area} = Atop + Abottom + Aside \] \[ \text{Surface Area} = 452.16 + 452.16 + 452.16 = 1356.48 \text{ square yards} \]

Thus, the surface area of the cylinder is approximately 1356.48 square yards when rounded to the nearest hundredth.