Question

The total surface area of a cone with slant height 21 m and diameter of its base 24 m is

• A. 252 π sq. m
• B. 504 π sq. m
• C. 396 π sq. m
• D. 1080 π sq. m

Answer 1

The Correct Option is C

The total surface area of a cone is given by the formula:

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

where:

• \( r \) is the radius of the base,
• \( l \) is the slant height.

Step 1: Given values

Diameter of the base = 24 m → Radius (\( r \)) = \( \frac{24}{2} = 12 \) m
Slant height (\( l \)) = 21 m

Step 2: Substituting into the formula

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

\[ = \pi (12) (21 + 12) \]

\[ = \pi (12) (33) \]

\[ = 396\pi \, \text{sq. m} \]

Final Answer: The total surface area of the cone is \( \mathbf{396\pi \, \text{sq. m}} \), which corresponds to option \( \mathbf{(3)} \).