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# Solution for A Spherical Ball of Lead 3 Cm in Diameter is Melted and Recast into Three Spherical Balls. If the Diameters of Two Balls Be A/2Cm and 2 Cm, Find the Diameter of the Third Ball. - CBSE Class 9 - Mathematics

ConceptVolume of a Sphere

#### Question

A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. If the diameters of two balls be a/2cm and 2 cm, find the diameter of the third ball.

#### Solution

Volume of lead ball = 4/3 πr^3

=4/3× 22/7×(3/2)^3

∴ According to question,

Volume of lead ball = 4/3×π(3/4)^3+4/3π(2/2)^3+4/3π(d/2)^3

⇒4/3π(3/2)^3=4/3π(3/4)^3+4/3[π(2/2)^3+(d/2)^3]

⇒4/3π[(3/2)^3]=4/3π[(3/4)^3+(2/2)^3+(d/2)^3]

⇒27/8=27/64+8/8+(d^3)/8

⇒ [27/8-27/64-1]8=d^3

⇒ d^3/8=125/64

⇒d/2=5/4

⇒d=10/4

⇒d=2.5cm

Is there an error in this question or solution?

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Solution A Spherical Ball of Lead 3 Cm in Diameter is Melted and Recast into Three Spherical Balls. If the Diameters of Two Balls Be A/2Cm and 2 Cm, Find the Diameter of the Third Ball. Concept: Volume of a Sphere.
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