Question

A birthday conical cap is cut by a plane parallel to it's base and the upper part us used as a new call cap for a toy. The curved surface area of this new cap is 1/9 of the curved surface area of the whole cone. Find the ratio of the line segments into which the cone's altitude is divided by the

Answer 1

Answer:

Step-by-step explanation:

Let the radius , height and slant height oa a conical cap be R, H and L units.

and ths radius, height and slant height of a new cone be r, h ,and l.

According to the question

πrl = 1/9 πRL

r/R × l/L = 1/9 ......(1)

In ΔADE and ΔABC

∠A =∠A ( common )

∠ADE =∠ABC ( corresponding angles)

∴ ΔADE ≅ ΔABC

SIMILARLY,

r/R =h/H=l /L

Putting the value in eq. (1)

h/H × h/H = 1/9

h/H = 1/3

H/h - 1 =3/1 -1

H-h /h = 3-2 /1

H- h /h = 2/1

so, the reaquired ratio is 2 :1