-
A sphere of radius r is inscribed in a right circular cone whose slant height equals twice the radius of the base a. What is the relation between r and a ?
-
-
r = a √2 -
r = a 3 -
r = a √3 - 3r = 2a
-
Correct Option: C
AB = 2a
BD = a
AD = √4a² - a²
= √3a² = √3a
= ∠AFO = 90°
OD = r
AO = √3a - r
| sin BAD = | = | ||
| 2a | 2 |
∠BAD = 30°
sin30°
| = | ⇒ | = | = | ||||
| OA | 2 | OA | √3a - r |
⇒ 2r = √3a - r
⇒ 3r = √3a
| ⇒ | ||
| √3 |
