Question
Download Solution PDFTwo right circular cones of height 16.4 cm and 17.2 cm respectively have base radius of 8.4 cm. These two cones are melted and recast into a sphere. Find the diameter of the sphere.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFAs we know,
Volume of the cone = (1/3) πr2h
Volume of sphere = (4/3) πR3
Height of first cone h1 = 16.4
Height of second cone h2 = 17.2 cm
Radius of both cone r1 and r2 is 8.4 cm
According to the question
Volume of sphere = sum of volumes of both cones
(4/3) πR3 = (1/3) π × 8.4 × 8.4 × 16.4 + (1/3) π × 8.4 × 8.4 × 17.2
⇒ (4/3) πR3 = (1/3) π × 8.4 × 8.4 (16.4 + 17.2)
⇒ R3 = (8.4 × 8.4 × 33.6)/4
⇒ R = ∛[8.4 × 8.4 × 8.4]
⇒ R = 8.4
∴ Diameter of the sphere = 2 × 8.4 = 16.8Last updated on Jun 16, 2025
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