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:
- Lateral surface area (rectangle) = \( 2\pi rh \)
- Area of the two bases = \( 2\pi r^2 \)
- 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.