Question

A cone is such that the area of its base equals its lateral surface area. If radius is r, find the slant height I.

• A. r
• B. 2r
• C. 3r
• D. 4r

Answer 1

Answer:

A. r

For a cone:

• Base area = $( \pi r^2 )$

• Lateral surface area = $( \pi r l )$(where (l) is slant height)

Given:

Base area = Lateral surface area

$\pi r^2 = \pi r l$

Cancel $( \pi r )$ (since (r \ne 0)):

r = l

Final Answer:

$\boxed{l = r}$