Find the total surface area of a cylinder with diameter of base 7 cm and height 40 cm.

Options

A. 1540 `cm^2`
B. 880 `cm^2`
C. 957 `cm^2`
D. 415 `cm^2`

Answer

To find the total surface area of a cylinder, we can follow these steps:

### Step 1: Identify the given values
- Diameter of the base of the cylinder (d) = 7 cm
- Height of the cylinder (h) = 40 cm

### Step 2: Calculate the radius of the base
The radius (r) is half of the diameter. Therefore, we can calculate it as:
\[ r = \frac{d}{2} = \frac{7 \, \text{cm}}{2} = 3.5 \, \text{cm} \]

### Step 3: Write down the formula for the total surface area of a cylinder
The formula for the total surface area (TSA) of a cylinder is given by:
\[ \text{TSA} = 2\pi r(h + r) \]
where \( \pi \) is approximately \( \frac{22}{7} \).

### Step 4: Substitute the values into the formula
Now, substituting the values of \( r \) and \( h \) into the formula:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 3.5 \times (40 + 3.5) \]

### Step 5: Simplify the expression
First, calculate \( 40 + 3.5 \):
\[ 40 + 3.5 = 43.5 \]
Now substitute this back into the TSA formula:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 3.5 \times 43.5 \]

### Step 6: Calculate the numerical values
Calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now calculate \( 3.5 \times 43.5 \):
\[ 3.5 \times 43.5 = 152.25 \]
Now, substitute this back into the TSA formula:
\[ \text{TSA} = \frac{44}{7} \times 152.25 \]

### Step 7: Perform the multiplication
Calculating \( \frac{44 \times 152.25}{7} \):
\[ 44 \times 152.25 = 6702 \]
Now divide by 7:
\[ \text{TSA} = \frac{6702}{7} \approx 957.43 \, \text{cm}^2 \]

### Final Result
The total surface area of the cylinder is approximately \( 957 \, \text{cm}^2 \).