What is the total surface area (in `cm^(2)`) of a cylinder having radius of base as 7 cm and height as 15 cm ?

Options

A. 814
B. 616
C. 968
D. 780

Answer

To find the total surface area of a cylinder, we can use the formula:

\[ \text{Total Surface Area} = 2\pi r(h + r) \]

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \) or \( 3.14 \).

Given:
- Radius \( r = 7 \) cm
- Height \( h = 15 \) cm

### Step 1: Substitute the values into the formula

Substituting the values of \( r \) and \( h \) into the total surface area formula:

\[ \text{Total Surface Area} = 2 \times \frac{22}{7} \times 7 \times (15 + 7) \]

### Step 2: Simplify the expression inside the parentheses

Calculate \( (15 + 7) \):

\[ 15 + 7 = 22 \]

### Step 3: Substitute back into the formula

Now substitute back into the formula:

\[ \text{Total Surface Area} = 2 \times \frac{22}{7} \times 7 \times 22 \]

### Step 4: Cancel out the \( 7 \) in the numerator and denominator

The \( 7 \) in the numerator and denominator cancels out:

\[ \text{Total Surface Area} = 2 \times 22 \times 22 \]

### Step 5: Calculate the multiplication

Now calculate \( 2 \times 22 \):

\[ 2 \times 22 = 44 \]

Now calculate \( 44 \times 22 \):

\[ 44 \times 22 = 968 \]

### Step 6: Final result

Thus, the total surface area of the cylinder is:

\[ \text{Total Surface Area} = 968 \, \text{cm}^2 \]

### Conclusion

The total surface area of the cylinder is \( 968 \, \text{cm}^2 \).

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