find the total surface area of a solid hemisphere of radius 7 cm. (Take it to be 3.142)

To find the total surface area of a solid hemisphere, we need to consider both the curved surface area and the flat circular base of the hemisphere.

### Step-by-Step Solution

1. **Curved Surface Area of Hemisphere:**

   The formula for the curved surface area of a hemisphere is:

   \[
   \text{Curved Surface Area} = 2 \pi r^2
   \]

2. **Area of the Base:**

   The base of the hemisphere is a circle with the same radius \( r \). The area of the base is:

   \[
   \text{Base Area} = \pi r^2
   \]

3. **Total Surface Area of the Hemisphere:**

   The total surface area is the sum of the curved surface area and the base area:

   \[
   \text{Total Surface Area} = 2 \pi r^2 + \pi r^2 = 3 \pi r^2
   \]

   Now, substitute the given values:

   \[
   r = 7 \, \text{cm}, \quad \pi = 3.142
   \]

   So,

   \[
   \text{Total Surface Area} = 3 \times 3.142 \times (7)^2
   \]

   Calculate \( 7^2 \):

   \[
   7^2 = 49
   \]

   Now substitute this value:

   \[
   \text{Total Surface Area} = 3 \times 3.142 \times 49
   \]

   Compute the multiplication:

   \[
   \text{Total Surface Area} = 3 \times 154.958 = 464.874 \, \text{cm}^2
   \]

### Final Answer

The total surface area of the solid hemisphere is **464.874 cm²**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the surface area change if the radius were doubled?
2. What is the volume of a hemisphere with the same radius?
3. How do you find the surface area of a hollow hemisphere?
4. How does the use of different values for \( \pi \) affect the calculation?
5. Can you derive the formula for the surface area of a hemisphere from scratch?

**Tip:** Remember that for surface area calculations, always double-check which parts of the solid are included (like bases or curves) in the final measurement.

Learn how to calculate the total surface area of a solid hemisphere with a radius of 7 cm using the formula for curved surface area and the area of the base. The step-by-step solution includes the use of π as 3.142. Suitable for Grades 8-10 geometry students.

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