What is the surface area of this cylinder? The radius is 9.7 yd and the height is 5.4 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

1 answer

To calculate the surface area of a cylinder, we will use the formula:

\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \]

Step 1: Calculate the areas of the top and bottom circles

The area of a circle is given by the formula:

\[ A = \pi r^2 \]

Since both the top and bottom are circles with the same radius (r = 9.7 yd):

\[ A_{\text{top}} = A_{\text{bottom}} = \pi (9.7)^2 \] Using \(\pi \approx 3.14\):

\[ A_{\text{top}} = A_{\text{bottom}} = 3.14 \times (9.7)^2 \] Calculating \( (9.7)^2 \):

\[ (9.7)^2 = 94.09 \]

Now calculate the area:

\[ A \approx 3.14 \times 94.09 \approx 295.73 \text{ yd}^2 \] Thus,

\[ A_{\text{top}} \approx 295.73 \text{ yd}^2 \] \[ A_{\text{bottom}} \approx 295.73 \text{ yd}^2 \]

Step 2: Calculate the area of the side (curved surface area)

First, we need to find the circumference of the top circle, which is given by:

\[ C = 2\pi r \] Substituting \( r = 9.7 \) yd:

\[ C = 2 \times 3.14 \times 9.7 \]

Calculating:

\[ C \approx 2 \times 3.14 \times 9.7 \approx 60.12 \text{ yd} \]

Now, the area of the side (curved surface area) is given by:

\[ A_{\text{side}} = C \times h \] Where \( h = 5.4 \) yd. Thus:

\[ A_{\text{side}} = 60.12 \times 5.4 \]

Calculating:

\[ A_{\text{side}} \approx 324.65 \text{ yd}^2 \]

Step 3: Calculate the total surface area

Adding all areas together:

\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \] \[ \text{Surface Area} \approx 295.73 + 295.73 + 324.65 \] \[ \text{Surface Area} \approx 916.11 \text{ yd}^2 \]

Final Answer:

The surface area of the cylinder is approximately 916.11 square yards.