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Question

The curved surface area of the frustum of a cone is 180 sq. cm and the circumference of its circular bases are 18 cm and 6 cm respectively. Find the slant height of the frustum of a cone.

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Solution

Let the radii of the circular ends be r1 cm and r2 cm.
Given:
Curved surface area of the frustum of the cone = 180 cm2
Also,
Circumference of the small end (C1) = 6 cm
2π r1 = 6
r1= 3π
And,
Circumference of the large end (C2) = 18 cm
2π r2 = 18
r2= 9π
Now,
Curved surface area of the frustum of the cone = π(r1 + r2)l
180 = π3π+9πl
180 = 12l
l = 15 cm

Thus, the slant height of the frustum of the cone is 15 cm.

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