The total surface area of a right circular cylinder with radius of the base 7 cm and height 20 cm, is :

Options

A. `900 cm^(2)`
B. `140 cm^(2)`
C. `1000 cm^(2)`
D. `1188 cm^(2)`

Answer

To find the total surface area of a right circular 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 3.14 (or you can use \(\frac{22}{7}\) for calculations)

Given:
- Radius \( r = 7 \) cm
- Height \( h = 20 \) cm

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

\[ \text{Total Surface Area} = 2\pi r(h + r) = 2\pi \times 7 \times (20 + 7) \]

### Step 2: Calculate \( h + r \)

\[ h + r = 20 + 7 = 27 \]

### Step 3: Substitute \( h + r \) back into the formula

\[ \text{Total Surface Area} = 2\pi \times 7 \times 27 \]

### Step 4: Calculate \( 2 \times 7 \)

\[ 2 \times 7 = 14 \]

### Step 5: Now multiply \( 14 \) by \( 27 \)

\[ 14 \times 27 = 378 \]

### Step 6: Now multiply by \( \pi \) (using \(\frac{22}{7}\) for \(\pi\))

\[ \text{Total Surface Area} = 378 \times \frac{22}{7} \]

### Step 7: Calculate \( 378 \times 22 \)

\[ 378 \times 22 = 8316 \]

### Step 8: Divide by \( 7 \)

\[ \frac{8316}{7} = 1188 \]

### Final Answer

\[ \text{Total Surface Area} = 1188 \, \text{cm}^2 \]