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Let the Height of the larger cone = H
Let the height of the smaller cone = h
Let the radius of the Larger cone = R
Let the radius of the smaller circle = r
h/H = r/R = l/L[ Similar triangles]
Curved Surface area of the frustum = (8/9) Curved surface area of the cone.
pi(R + r)(L – l) = (8/9)piRL
(1 + r/R)(1 – l/L) = (8/9)
(1 + h/H)(1 – h/H ) = (8/9)
On simplifying, we get h2/H2 = 1/9
Therefore h/H = 1/3
Therefore h/(H- h) = 1/2
Let the height of the smaller cone = h
Let the radius of the Larger cone = R
Let the radius of the smaller circle = r
h/H = r/R = l/L[ Similar triangles]
Curved Surface area of the frustum = (8/9) Curved surface area of the cone.
pi(R + r)(L – l) = (8/9)piRL
(1 + r/R)(1 – l/L) = (8/9)
(1 + h/H)(1 – h/H ) = (8/9)
On simplifying, we get h2/H2 = 1/9
Therefore h/H = 1/3
Therefore h/(H- h) = 1/2
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