A right circular cone of height h and radius R is cut by a plane parallel to the base at a distance h/5 from the base. The ratio of the curved surface area of the frustum and the total surface area of the resulting cone is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 9L : 16(L + R).
Let L = √(R² + h²)
Curved surface area of frustum = (9/25)πRL
Total surface area of the smaller cone = (16/25)πRL + (16/25)πR² = (16/25)πR(L + R)
Ratio = [ (9/25)πRL] : [ (16/25)πR(L + R) ] = 9L : 16(L + R)