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?
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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
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