A cone has base radius 6 cm and slant height 10 cm. If a conical frustum is cut from it, the top radius is 3 cm and height is proportionally scaled. Find the height of the frustum.
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Correct answer: A
Explanation
R = 6 cm
l = 10 cm
r = 3 cm
Similar Triangles ⇒ h₁ / h = r / R
h₁ / h = 3 / 6 = 1/2
Height of the smaller cone = h/2
Now, the height of the larger cone:
h = √(l² − R²)
= √(10² − 6²)
= √(100 − 36)
= √64
= 8
⇒ Height of the smaller cone = 8/2 = 4
⇒ Height of the frustum = 8 − 4 = 4 cm