What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm?

Options

A. 10 cm
B. 12 cm
C. 15 cm
D. 16 cm

Answer

To find the height of a solid cylinder given its radius and total surface area, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for the total surface area of a cylinder**:
The total surface area (TSA) of a cylinder is given by the formula:
\[ \text{TSA} = 2\pi r (r + h) \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

2. **Substitute the known values into the formula**:
We are given:
- Radius \( r = 5 \) cm
- Total Surface Area \( \text{TSA} = 660 \) cm²
Substituting these values into the formula:
\[ 660 = 2 \pi (5)(5 + h) \]

3. **Use the value of \( \pi \)**:
For this calculation, we will use \( \pi \approx \frac{22}{7} \). Thus, the equation becomes:
\[ 660 = 2 \times \frac{22}{7} \times 5 \times (5 + h) \]

4. **Simplify the equation**:
First, calculate \( 2 \times \frac{22}{7} \times 5 \):
\[ 2 \times \frac{22}{7} \times 5 = \frac{220}{7} \]
Now, substitute this back into the equation:
\[ 660 = \frac{220}{7} (5 + h) \]

5. **Multiply both sides by 7 to eliminate the fraction**:
\[ 660 \times 7 = 220(5 + h) \]
\[ 4620 = 220(5 + h) \]

6. **Divide both sides by 220**:
\[ \frac{4620}{220} = 5 + h \]
Simplifying \( \frac{4620}{220} \):
\[ 21 = 5 + h \]

7. **Solve for \( h \)**:
\[ h = 21 - 5 = 16 \text{ cm} \]

### Final Answer:
The height of the cylinder is \( 16 \) cm.

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