The radius of a hemisphere is 2.5 cm. Find its total surface area.

Answer

To find the total surface area of a hemisphere with a radius of 2.5 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 hemisphere is given by the formula:
\[ \text{TSA} = 3\pi r^2 \]
where \( r \) is the radius of the hemisphere.

### Step 2: Identify the radius.
From the question, we know that the radius \( r = 2.5 \) cm.

### Step 3: Substitute the radius into the formula.
Now, we will substitute the value of the radius into the formula:
\[ \text{TSA} = 3\pi (2.5)^2 \]

### Step 4: Calculate \( (2.5)^2 \).
First, we calculate \( (2.5)^2 \):
\[ (2.5)^2 = 6.25 \]

### Step 5: Substitute \( (2.5)^2 \) back into the formula.
Now substituting back into the TSA formula:
\[ \text{TSA} = 3\pi (6.25) \]

### Step 6: Multiply 3 and 6.25.
Next, we calculate:
\[ 3 \times 6.25 = 18.75 \]

### Step 7: Multiply by \( \pi \).
Now, we will use \( \pi \approx 3.14 \) for our calculations:
\[ \text{TSA} = 18.75 \times 3.14 \]

### Step 8: Calculate the final result.
Now, we perform the multiplication:
\[ 18.75 \times 3.14 = 58.875 \]

### Conclusion:
Thus, the total surface area of the hemisphere is:
\[ \text{TSA} = 58.875 \, \text{cm}^2 \]

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