To calculate the surface area of a right circular cylinder, you need to find the area of the two circular bases and the lateral (side) surface area.
-
Area of the circular bases: The area of one base is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius of the base.
Given that the diameter of the cylinder's top is 1.5 cm, the radius \( r \) will be half of the diameter: \[ r = \frac{1.5}{2} = 0.75 \text{ cm} \]
Now, the area of one base: \[ A = 3.14 \times (0.75)^2 = 3.14 \times 0.5625 = 1.76625 \text{ cm}^2 \]
The total area of the two bases is: \[ \text{Total area of bases} = 2 \times 1.76625 = 3.5325 \text{ cm}^2 \]
-
Lateral surface area: The lateral surface area of the cylinder is calculated using the formula: \[ A = 2\pi rh \] where \( h \) is the height of the cylinder.
Given \( h = 4 \text{ cm} \): \[ A = 2 \times 3.14 \times 0.75 \times 4 = 2 \times 3.14 \times 3 = 18.84 \text{ cm}^2 \]
-
Total surface area: Now, add the area of the bases and the lateral area together: \[ \text{Total surface area} = \text{Total area of bases} + \text{Lateral surface area} = 3.5325 + 18.84 = 22.3725 \text{ cm}^2 \]
Finally, let’s round the answer to the nearest tenth: \[ \text{Total surface area} \approx 22.4 \text{ cm}^2 \]
Since this isn't one of the response options you've provided, it seems either additional information about the calculation is needed, or there might have been a misunderstanding regarding the dimensions. Based on the provided dimensions, please verify if they are correctly interpreted, or if you would like additional assistance.