Question

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

Answer 1

Answer:

The slant height would be 12 -4√3

Step-by-step explanation:

Ratio b/w CSA of upper cone to lower portion = 1 : 2

Ratio b/w CSA of upper cone to total cone = 1 : 3

CSA = π x r x l

l = 12 cm

Curved Area of cone = 48 x π

Curved Area of small cone = 16 x π

Let x would be the ratio by which r and l have been reduced.

x^2 x 48 x π = 16π

x = 1/ √3

l of small cone = 12/ √3

l of lower portion = 12 - 12/ √3

= 12 x ( √3 -1/ √3)

= 12 x (3 - √3 / 3)

= 12 -4√3