Question

Calculate the surface area of the net diagram of the right circular cylinder. Use 3.14 for π
the circual is 1.5 cm
the rectnagle is 4 cm
Round your answer to the nearest tenths place.

(1 point)
Responses

51.8 cm2
51.8 cm 2

382.6 cm2
382.6 cm 2

171.3 cm2
171.3 cm 2

49.3 cm2

Answer 1

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

The formulas for the surface area of a cylinder are:

1. Lateral surface area (rectangle) = \( 2\pi rh \)
2. Area of the two bases = \( 2\pi r^2 \)
3. Total surface area = Lateral surface area + Area of the two bases = \( 2\pi rh + 2\pi r^2 \)

Given:
- Radius \( r = 1.5 \, \text{cm} \)
- Height \( h = 4 \, \text{cm} \)
- Use \( \pi = 3.14 \)

**Step 1: Calculate the lateral surface area**
\[
\text{Lateral surface area} = 2\pi rh = 2 \times 3.14 \times 1.5 \times 4
\]
\[
= 2 \times 3.14 \times 6 = 2 \times 18.84 = 37.68 \, \text{cm}^2
\]

**Step 2: Calculate the area of the two bases**
\[
\text{Area of the two bases} = 2\pi r^2 = 2 \times 3.14 \times (1.5^2)
\]
\[
= 2 \times 3.14 \times 2.25 = 2 \times 7.065 = 14.13 \, \text{cm}^2
\]

**Step 3: Calculate the total surface area**
\[
\text{Total surface area} = \text{Lateral surface area} + \text{Area of the two bases}
\]
\[
= 37.68 + 14.13 = 51.81 \, \text{cm}^2
\]

Rounding to the nearest tenths place, the total surface area is:

\[
\text{Total surface area} \approx 51.8 \, \text{cm}^2
\]

Thus, the answer is **51.8 cm²**.