Question

If the curved surface area of a cone is 880 cm\(^2\) and its radius is 14 cm, then its slant height is

• A. 10 cm
• B. 20 cm
• C. 40 cm
• D. 30 cm

Hint:

When the radius or diameter is a multiple of 7, it's almost always easier to use \(\pi = 22/7\) as it will lead to cancellations and simpler arithmetic.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The curved surface area (CSA) of a cone is related to its radius (\(r\)) and slant height (\(l\)) by a standard formula. We can use this formula to find the slant height when the area and radius are known.

Step 2: Key Formula or Approach:
The formula for the curved surface area of a cone is:
\[ CSA = \pi r l \] We need to solve for \(l\).

Step 3: Detailed Explanation:
We are given:
CSA = 880 cm\(^2\)
Radius, \(r = 14\) cm
Use the value \(\pi \approx \frac{22}{7}\).
Substitute the given values into the formula:
\[ 880 = \frac{22}{7} \times 14 \times l \] Simplify the right side:
\[ 880 = 22 \times 2 \times l \] \[ 880 = 44 \times l \] Now, solve for \(l\):
\[ l = \frac{880}{44} \] \[ l = 20 \] The slant height is 20 cm.

Step 4: Final Answer:
The slant height is 20 cm.