Question

What is the surface area of this cylinder? The radius is 5 in and the height is 9 in 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 inches

Answer 1

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

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

Where:
- \(A_{\text{top}}\) and \(A_{\text{bottom}}\) are the areas of the top and bottom circles,
- \(A_{\text{side}}\) is the area of the side of the cylinder.

1. **Area of the top and bottom circles:**
The area \(A\) of a circle is given by the formula:
\[
A = \pi r^2
\]
Where \(r\) is the radius. The radius \(r\) is 5 inches.

So, the area of one circle is:
\[
A = \pi (5)^2 = \pi \cdot 25 = 25\pi
\]

Thus, the combined area of the top and bottom is:
\[
A_{\text{top}} + A_{\text{bottom}} = 25\pi + 25\pi = 50\pi
\]

2. **Area of the side:**
The area of the side (the lateral surface area) of the cylinder is given by the formula:
\[
A_{\text{side}} = 2\pi rh
\]
Where \(h\) is the height of the cylinder (9 inches).

Substituting the values:
\[
A_{\text{side}} = 2\pi (5)(9) = 90\pi
\]

3. **Total Surface Area:**
Now we combine all the areas to find the total surface area:
\[
\text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 50\pi + 90\pi = 140\pi
\]

4. **Calculating with \(\pi \approx 3.14\):**
Now we substitute the value of \(\pi\):
\[
\text{Surface Area} \approx 140 \cdot 3.14 = 439.6
\]

5. **Rounding:**
Rounding \(439.6\) to the nearest hundredth, we get:
\[
\text{Surface Area} \approx 439.60 \text{ square inches}
\]

So, the surface area of the cylinder is about **439.60 square inches**.