Question

if curved surface of frustum is 8 upon 9 of curved surface area of whole cone find the ratio of the line segments into which the altitude of cone is divided by plane

Answer 1

Answer:

2: 1

Step-by-step explanation:

Let R is the radius , H is the height and L is the slant height of the cone

Let r is the radius , h is the height  and l is the slant height of smaller cone .

Now, Δ OAB and Δ OCD

∠OAB = ∠OCD ( each 90°)

∠AOB = ∠COD ( common )

AB = CD ( parallel sides are equal )

Δ OAB ≅ ΔOCD (ASA)

OB /OD = AB / CD = OA /OC

curved surface area of the smaller cone = curved surface area of cone - curved surface area of frustum

curved surface area of smaller cone = (1- 8/9) × curved surface area of cone

curved surface area of smaller cone / curved surface area of cone = 1/9

πrl/πRL =1/9

rl/ RL = 1/9

r/R × l /L = 1/9

h/H ×h/H = 1/9

(h/H )² = 1/9

h/H = √1/9

h/H = 1/3

h =H/3

Now , OA /AC = h / (h-h )

=(H/3) / ( H-H/3)

=(H/3)(2H/3)

=1/2

=OA : AC = 1:2