XAT 2018 — QA & DI Question 18
A cone of radius 4 cm with a slant height of 12 cm was sliced horizontally, resulting into a smaller cone (upper portion) and a frustum (lower portion). If the ratio of the curved surface area of the upper smaller cone and the lower frustum is 1:2, what will be the slant height of the frustum?
Answer & solution
- A
12 - √3
- B
12 - 2√3
- C
12 - 3√3
12 - 4√3
- E
None of the above
Curved surface area of the original larger cone = π × Radius × Slant height = 48π
Therefore, the curved surface of the smaller cone = 1/3 × 48π = 16π
Now, the radius and slant of height of the smaller cone would be reduced in equal proportions from the larger cone.
Therefore, slant height of the frustum would be 1/√3 time the corresponding values of the larger cone.
⇒ Slant height of the smaller cone = 1/√3 × 12 = 4√3
∴ Slant height of the frustum = 12 - 4√3
Hence, option (d).