NCERT · Class 9 · Mathematics · Surface Areas and VolumesThe slant height ($l$) of a cone is related to its radius ($r$) and height ($h$) by the formula:
Step-by-Step Solution
In a right circular cone, the height, radius, and slant height form a right-angled triangle where the slant height is the hypotenuse. By Pythagoras theorem, $l^2 = r^2 + h^2$, which means $l = \sqrt{r^2 + h^2}$. Therefore, the correct option is $l = \sqrt{r^2 + h^2}$.
Detailed Options Breakdown
Option : l = r + h
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
Option 1: l = \sqrt{h^2 - r^2}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
Option 2: l = \sqrt{r^2 + h^2} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: l = r^2 + h^2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
💡 Study Guide: This question tests core syllabus concepts from Surface Areas and Volumes. For formulas, key summaries, and mock exam reference guides, read the full Surface Areas and Volumes Revision Notes.