Find the total surface area of a hemispherical bowl of radius 5 cm .

Answer

To find the total surface area of a hemispherical bowl with a radius of 5 cm, we can follow these steps:

### Step 1: Understand the formula for the total surface area of a hemisphere.
The total surface area (TSA) of a hemispherical bowl is given by the formula:
\[ \text{TSA} = 3 \pi r^2 \]
This formula accounts for the curved surface area of the hemisphere and the area of the circular base.

### Step 2: Identify the radius.
In this case, the radius \( r \) of the hemispherical bowl is given as 5 cm.

### Step 3: Substitute the radius into the formula.
Now, we can substitute \( r = 5 \) cm into the formula:
\[ \text{TSA} = 3 \pi (5)^2 \]

### Step 4: Calculate \( (5)^2 \).
Calculating \( (5)^2 \):
\[ (5)^2 = 25 \]

### Step 5: Substitute back into the formula.
Now substitute \( 25 \) back into the TSA formula:
\[ \text{TSA} = 3 \pi \times 25 \]

### Step 6: Multiply the values.
Now, multiply \( 3 \) and \( 25 \):
\[ 3 \times 25 = 75 \]
So, we have:
\[ \text{TSA} = 75 \pi \]

### Step 7: Write the final answer with units.
Thus, the total surface area of the hemispherical bowl is:
\[ \text{TSA} = 75 \pi \, \text{cm}^2 \]

### Summary of the Solution:
The total surface area of the hemispherical bowl with a radius of 5 cm is \( 75 \pi \, \text{cm}^2 \).

---