Share

Books Shortlist

# 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 3/2cm 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

Therefore, the diameter of the third ball is 2.5cm .

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 21: Surface Areas and Volume of a Sphere
Ex.21.20 | Q: 7 | Page no. 20
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.
S