A hollow cone is cut by a plane parallel to the base and the upper part is removed. If the curved surface of the remainder is 15/16 of the curved surface of the whole cone , find the ratio of the line segments into which the cone’s attitude is divided by the plane.

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1: 3

2:3

1:1

5:1

answer is A.

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Detailed Solution

Let H be the height of the cone , R is the radius
Let’s consider cone is cut at height h
∴ ℎ = 1
𝐻 𝑚
Using ration ℎ = 1
𝐻 𝑚
𝑟 = 1 and 𝐼 = 1

(ΔBDF and ΔBEC are similar triangles)
𝑅 𝑚 𝐿 𝑚
Remaining curved surface area is 15 times
16
The original surface area

1 𝜋𝑟𝑙
⇒ 16 = 𝜋𝑅𝐿

𝑟
= 𝑅

𝐼
× 𝐿

1
= 𝑚

1
× 𝑚
1 1
⇒ 16 = 𝑚
1 2

1
× 𝑚
1 2
⇒ ( )
4

= (𝑚)
1 1
⇒ 𝑚 = 4
1 ℎ 1
H = 4h

⇒ 𝑚 = 𝐻 = 4
ℎ
We have to find the ratio of attitudes of removed and remaining i .e − ℎ
𝐻
Now, we will substitute the value of H = 4h
ℎ
Ratio = − ℎ
4ℎ
ℎ
=
3ℎ
= 1
3

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