What is the surface area of this cylinder?

Question

The radius is 6 yd and the height is 11 yd
Surface area = Atop + Abottom + Aside
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
The surface area of the cylinder is about _____ square yards

Answer 1

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

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

Where:

• $A_{\text{top}}=\pi r^2$ (area of the top circle)
• $A_{\text{bottom}}=\pi r^2$ (area of the bottom circle)
• $A_{\text{side}}=2\pi rh$ (area of the side)

Given:

• Radius $r=6$ yd
• Height $h=11$ yd
• Use $\pi \approx 3.14$

Now, calculate each part:

1. Area of the top and bottom circles: $$A_{\text{top}}=A_{\text{bottom}}=\pi r^2=3.14\times (6^2)=3.14\times 36=113.04,\text{square yards}$$

   So, $$A_{\text{top}}+A_{\text{bottom}}=113.04+113.04=226.08,\text{square yards}$$

2. Area of the side: $$A_{\text{side}}=2\pi rh=2\times 3.14\times 6\times 11$$

   First, calculate $2\times 6=12$: $$A_{\text{side}}=12\times 3.14\times 11$$ Now calculate $3.14\times 11=34.54$: $$A_{\text{side}}=12\times 34.54=414.48,\text{square yards}$$

3. Total Surface Area: $$\text{Surface Area}=A_{\text{top}}+A_{\text{bottom}}+A_{\text{side}}=226.08+414.48=640.56,\text{square yards}$$

Finally, rounding to the nearest hundredth, the surface area of the cylinder is:

$$\boxed{{\displaystyle 640.56}},\text{square yards}$$