The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is ……………. .

Options

A. `160 picm^2`
B. `168 pi cm^2`
C. `120 pi cm^2`
D. `136 pi cm^2`

Answer

To find the curved surface area of a right circular cone with a height of 15 cm and a base diameter of 16 cm, we can follow these steps:

### Step 1: Determine the radius of the base.
The radius \( r \) is half of the diameter. Given that the diameter is 16 cm:
\[ r = \frac{16}{2} = 8 \text{ cm} \]

### Step 2: Identify the height of the cone.
The height \( h \) is given as:
\[ h = 15 \text{ cm} \]

### Step 3: 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 4: Use the formula for the curved surface area of the cone.
The formula for the curved surface area \( A \) of a cone is:
\[ A = \pi r l \]
Substituting the values of \( r \) and \( l \):
\[ A = \pi \times 8 \times 17 \]

### Step 5: Calculate the curved surface area.
\[ A = 136\pi \text{ cm}^2 \]

### Final Answer:
The curved surface area of the right circular cone is \( 136\pi \text{ cm}^2 \).

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