Question

If the radius of the base of a cone is 7 cm and the height is 24 cm, find its slant height:

• A. 23 cm
• B. 26 cm
• C. 31 cm
• D. 25 cm

Hint:

In right circular cones, always use the Pythagoras theorem: $l = \sqrt{r^2 + h^2}$ to find the slant height.

Answer 1

The Correct Option is B

Step 1: Recall the formula for the slant height of a cone.
For a cone with radius $r$ and height $h$, the slant height $l$ is given by the Pythagoras theorem as:
\[ l = \sqrt{r^2 + h^2} \]
Step 2: Substitute the given values.
Given $r = 7$ cm and $h = 24$ cm, substitute into the formula:
\[ l = \sqrt{7^2 + 24^2} \] \[ l = \sqrt{49 + 576} = \sqrt{625} \]
Step 3: Simplify.
\[ l = 25 \, \text{cm} \]
Step 4: Conclusion.
The slant height of the cone is 25 cm.