Question

Calculate the surface area of the net diagram of the right circular cylinder. Use 3.14 for π
circul 5 inches
rectangle 4 inches
(1 point)
Responses

157 inches2
157 inches 2

282.6 inches2
282.6 inches 2

141.3 inches2
141.3 inches 2

197 inches2

Answer 1

To calculate the surface area of a right circular cylinder, we need to consider both the lateral surface area and the area of the two circular bases.

1. **Lateral Surface Area**: The lateral surface area (A_lateral) of a cylinder can be calculated using the formula:
\[
A_{\text{lateral}} = 2\pi rh
\]

Where \( r \) is the radius and \( h \) is the height.

Given:
- Diameter of the cylinder = 5 inches, so the radius \( r = \frac{5}{2} = 2.5 \) inches.
- Height \( h = 4 \) inches.

Now substitute the values:
\[
A_{\text{lateral}} = 2 \times 3.14 \times 2.5 \times 4
\]
\[
A_{\text{lateral}} = 2 \times 3.14 \times 10 = 62.8 \text{ inches}^2
\]

2. **Area of the Bases**: The area of one circular base (A_base) is given by the formula:
\[
A_{\text{base}} = \pi r^2
\]

Therefore, the total area of the two bases is:
\[
A_{\text{bases}} = 2 \times \pi r^2
\]

Substituting the radius:
\[
A_{\text{bases}} = 2 \times 3.14 \times (2.5)^2
\]
\[
A_{\text{bases}} = 2 \times 3.14 \times 6.25 = 39.25 \text{ inches}^2
\]

3. **Total Surface Area**: Now add the lateral area and the area of the two bases:
\[
A_{\text{total}} = A_{\text{lateral}} + A_{\text{bases}}
\]
\[
A_{\text{total}} = 62.8 + 39.25 = 102.05 \text{ inches}^2
\]

It appears that none of the provided answer choices match this calculated surface area of the right circular cylinder. There may be an error in the provided options, or further checking might be necessary.

If we calculate it again based on other interpretations or adjustments, please let me know!