The radius of the base of a solid right circular cone is 8 cm and its height is 15 cm. The total surface area of the cone is:

Options

A. 128 `pi`
B. `200 pi`
C. `136 pi`
D. `120 pi`

Answer

To find the total surface area of a solid right circular cone, we can use the formula:

\[ \text{Total Surface Area} = \pi r l + \pi r^2 \]

where:
- \( r \) is the radius of the base,
- \( l \) is the slant height of the cone.

### Step 1: Identify the given values
From the problem, we have:
- Radius \( r = 8 \) cm
- Height \( h = 15 \) cm

### Step 2: Calculate the slant height \( l \)
The slant height \( l \) can be calculated using the Pythagorean theorem:

\[ l = \sqrt{r^2 + h^2} \]

Substituting the values of \( r \) and \( h \):

\[ l = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \text{ cm} \]

### Step 3: Substitute the values into the total surface area formula
Now that we have \( r \) and \( l \), we can substitute these values into the total surface area formula:

\[ \text{Total Surface Area} = \pi r l + \pi r^2 \]

Substituting \( r = 8 \) cm and \( l = 17 \) cm:

\[ \text{Total Surface Area} = \pi (8)(17) + \pi (8^2) \]

### Step 4: Calculate each term
Calculating the first term:

\[ \pi (8)(17) = 136\pi \]

Calculating the second term:

\[ \pi (8^2) = \pi (64) = 64\pi \]

### Step 5: Combine the terms
Now we can combine both terms:

\[ \text{Total Surface Area} = 136\pi + 64\pi = 200\pi \]

### Step 6: Final answer
Thus, the total surface area of the cone is:

\[ \text{Total Surface Area} = 200\pi \text{ cm}^2 \]