-
A sphere has the same curved surface area as a cone of vertical height 40 cm and radius 30 cm. The radius of the sphere is
-
- 5√5 cm
- 5√3 cm
- 5√15 cm
- 5√10 cm
Correct Option: C
Slant height of cone (l) = √h² + r²
= √30² + 40² = √900 + 1600
= √2500 = 50 cm.
∴ Curved surface area of cone = πrl = (π × 30 × 50) sq. cm.
= 1500π sq. cm.
If the radius of sphere be R cm, then 4πR² = 1500π
| ⇒ R² = | = 375 | |
| 4 |
⇒ R = √375 = √5 × 5 × 15
= 5√15 cm.
