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# Solution for An Iron Spherical Ball Has Been Melted and Recast into Smaller Balls of Equal Size. If the Radius of Each of the Smaller Balls is 1/4 of the Radius of the Original Ball, How Many Such Balls Are Made? Compare the Surface Area, of All the Smaller Balls Combined Together With That of the Original Ball. - CBSE Class 10 - Mathematics

ConceptVolume of a Combination of Solids

#### Question

An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

#### Solution

Given that radius of each of smaller ball

Let radius of smaller ball be . r

Radius of bigger ball be 4r

Volume of big spherical ball =4/3pir^3    (∵ r = 4r)

V_1 = 4/3pi(4r)^3      ............(1)

Volume of each small ball = 4/3pir^3

v_2=4/3PIR^3          .............(2)

Let no of balls be 'n'

n = V_1/V_2

⇒ n=(4/3pi(4r)^3)/(4/3pi(r)^3)

⇒ n = 43 = 64

∴ No of small balls = 64

Curved surface area of sphere = 4πr2

Surface area of big ball (S1) = 4π(4r)2    ............(3)

Surface area of each small ball(S1) = 4πr2

Total surface area of 64 small balls

(S_2)=64xx4pir^2        ..............(4)

By combining (3) and (4)

⇒ S_2/3=4

⇒ S2 = 4s

∴Total surface area of small balls is equal to 4 times surface area of big ball.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Q: 29
Solution An Iron Spherical Ball Has Been Melted and Recast into Smaller Balls of Equal Size. If the Radius of Each of the Smaller Balls is 1/4 of the Radius of the Original Ball, How Many Such Balls Are Made? Compare the Surface Area, of All the Smaller Balls Combined Together With That of the Original Ball. Concept: Volume of a Combination of Solids.
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