A solid cone with curved surface area twice its base area has slant height of 6√3 cm. Its height is :
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 9 cm.
Slant height (I) of cone = √r2 + h2
CSA of cone = πrl
here, r = radius, h = height, and l = slant height
Now,
Let the radius of the cone be r units.
⇒ πrl = 2πr2
⇒ l = 2r
⇒ r = 6√3/2
⇒ r = 3√3
Slant height (I) of cone = √r2 + h2
⇒ (6√3)2 = (3√3)2 + h2
⇒ h2 = 108 - 27 = 81
⇒ h = 9 cm