Hemisphere Surface Area Calculation

To calculate the total surface area (TSA) of a hemisphere, we first need to determine its radius from the given diameter.

Given Hemisphere Details

• Diameter of the hemisphere, $d = 7$ cm.
• The radius ($r$) is half the diameter: $r = \frac{d}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm}$.

Surface Area Formula Recall

The formula for the total surface area (TSA) of a hemisphere is:

TSA $= 2 \pi r^2 + \pi r^2 = 3 \pi r^2$

Here, $r$ is the radius and we use the approximation $\pi \approx \frac{22}{7}$.

Step-by-Step Calculation

1. Substitute the radius ($r = 3.5$ cm) into the TSA formula:

   TSA $= 3 \times \frac{22}{7} \times (3.5 \text{ cm})^2$

2. Calculate the square of the radius:

   $(3.5 \text{ cm})^2 = 3.5 \times 3.5 \text{ cm}^2 = 12.25 \text{ cm}^2$

3. Multiply the terms:

   TSA $= 3 \times \frac{22}{7} \times 12.25 \text{ cm}^2$

   TSA $= 3 \times 22 \times \frac{12.25}{7} \text{ cm}^2$

   TSA $= 3 \times 22 \times 1.75 \text{ cm}^2$

   TSA $= 66 \times 1.75 \text{ cm}^2$

4. Compute the final value:

   TSA $= 115.5 \text{ cm}^2$

The total surface area of the hemisphere is $115.5 \text{ cm}^2$.