The radius of the base of a right cylinder is 14m and its height is 21m. Its total surface area is `:`

Options

A. 1848`m^(2)`
B. 1848 `m^(3)`
C. 3080` dm^(2)`
D. 3080 `m^(2)`

Answer

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

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

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

### Step 1: Identify the given values
- Radius \( r = 14 \, \text{m} \)
- Height \( h = 21 \, \text{m} \)

### Step 2: Substitute the values into the formula
\[ \text{Total Surface Area} = 2\pi r(h + r) = 2\pi \times 14 \times (21 + 14) \]

### Step 3: Calculate \( h + r \)
\[ h + r = 21 + 14 = 35 \]

### Step 4: Substitute \( h + r \) back into the formula
\[ \text{Total Surface Area} = 2\pi \times 14 \times 35 \]

### Step 5: Calculate \( 2 \times 14 \)
\[ 2 \times 14 = 28 \]

### Step 6: Now calculate \( 28 \times 35 \)
\[ 28 \times 35 = 980 \]

### Step 7: Substitute back into the formula
\[ \text{Total Surface Area} = 980\pi \]

### Step 8: Use the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Total Surface Area} = 980 \times \frac{22}{7} \]

### Step 9: Calculate \( 980 \times 22 \)
\[ 980 \times 22 = 21560 \]

### Step 10: Divide by 7
\[ \frac{21560}{7} = 3080 \]

### Final Answer
Thus, the total surface area of the cylinder is:
\[ \text{Total Surface Area} = 3080 \, \text{m}^2 \]