What is the total surface area and the curved surface area of a solid hemisphere of radius 14cm ?

Options

A. `924cm^(2),616cm^(2)`
B. `5544cm^(2),1848cm^(2)`
C. `1848cm^(2),1232cm^(2)`
D. `2772cm^(2),1848cm^(2)`

Answer

To find the total surface area and the curved surface area of a solid hemisphere with a radius of 14 cm, we can follow these steps:

### Step 1: Understand the formulas
- The **Total Surface Area (TSA)** of a hemisphere is given by the formula:
\[ \text{TSA} = 3\pi r^2 \]
- The **Curved Surface Area (CSA)** of a hemisphere is given by the formula:
\[ \text{CSA} = 2\pi r^2 \]

### Step 2: Substitute the radius into the formulas
Given that the radius \( r = 14 \) cm, we will substitute this value into the formulas.

### Step 3: Calculate the Total Surface Area
Using the TSA formula:
\[ \text{TSA} = 3\pi r^2 = 3\pi (14)^2 \]
Calculating \( (14)^2 \):
\[ (14)^2 = 196 \]
Now substituting this back into the TSA formula:
\[ \text{TSA} = 3\pi \times 196 \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{TSA} = 3 \times \frac{22}{7} \times 196 \]
Calculating \( 3 \times 22 = 66 \):
\[ \text{TSA} = \frac{66 \times 196}{7} \]
Now, calculate \( 66 \times 196 \):
\[ 66 \times 196 = 12936 \]
Now divide by 7:
\[ \text{TSA} = \frac{12936}{7} = 1848 \text{ cm}^2 \]

### Step 4: Calculate the Curved Surface Area
Using the CSA formula:
\[ \text{CSA} = 2\pi r^2 = 2\pi (14)^2 \]
Again, we know \( (14)^2 = 196 \):
\[ \text{CSA} = 2\pi \times 196 \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 196 \]
Calculating \( 2 \times 22 = 44 \):
\[ \text{CSA} = \frac{44 \times 196}{7} \]
Now, calculate \( 44 \times 196 \):
\[ 44 \times 196 = 8624 \]
Now divide by 7:
\[ \text{CSA} = \frac{8624}{7} = 1232 \text{ cm}^2 \]

### Final Answers
- Total Surface Area (TSA) = 1848 cm²
- Curved Surface Area (CSA) = 1232 cm²