The total surface area of a right circular cylinder whose height is 15 cm and the radius of the base is 7 cm, is

Options

A. 968 `cm^2`
B. 2310 `cm^2`
C. 488 `cm^2`
D. 1860 `cm^2`

Answer

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

### Step 1: Understand the formula for the total surface area of a cylinder.
The total surface area (TSA) of a right circular cylinder is given by the formula:
\[ \text{TSA} = 2\pi rh + 2\pi r^2 \]
where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

### Step 2: Identify the given values.
From the problem, we have:
- Height \( h = 15 \) cm
- Radius \( r = 7 \) cm

### Step 3: Substitute the values into the formula.
Now, we substitute the values of \( r \) and \( h \) into the TSA formula:
\[ \text{TSA} = 2\pi (7)(15) + 2\pi (7^2) \]

### Step 4: Calculate the curved surface area.
First, calculate the curved surface area:
\[ \text{Curved Surface Area} = 2\pi rh = 2\pi (7)(15) = 210\pi \]

### Step 5: Calculate the area of the two circular bases.
Next, calculate the area of the two circular bases:
\[ \text{Area of two bases} = 2\pi r^2 = 2\pi (7^2) = 2\pi (49) = 98\pi \]

### Step 6: Combine both areas to find the total surface area.
Now, we combine both areas:
\[ \text{TSA} = 210\pi + 98\pi = 308\pi \]

### Step 7: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \):
\[ \text{TSA} = 308 \times \frac{22}{7} \]

### Step 8: Perform the multiplication.
Calculating the multiplication:
\[ 308 \times \frac{22}{7} = \frac{308 \times 22}{7} = \frac{6766}{7} = 968 \text{ cm}^2 \]

### Final Answer:
The total surface area of the right circular cylinder is \( 968 \text{ cm}^2 \).

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