Question

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

Answer 1

Answer:

The diameter of the third ball is 5 cm.

Step-by-step explanation:

Given :  

Let the Radius of the third ball be r3

Radius of the spherical ball , R = 3 cm

Radius of the first ball, r1 = 1.5 cm

Radius of the second ball, r2 = 2 cm

Volume of the spherical ball, V =  4/3πR³

Volume of the spherical ball is equal to the volume of the 3 small spherical balls.

Volume of the spherical ball, V = Volume (V1) of first ball + Volume (V2) of second ball + Volume of third ball (V3)

4/3πR³ = 4/3πr1³ + 4/3πr2³ + 4/3πr3³

4/3πR³ = 4/3π (r1³ + r2³ + r3³)

R³ = (r1³ + r2³ + r3³)

3³ = (1.5³ + 2³ + r3³)

27 = 3.375 + 8 + r3³

27 = 11.375 + r3³

r3³ = 27 - 11.375

r3³ = 15.625

r3 = ³√15.625

r3 = ³√ 2.5 × 2.5 × 2.5

r3 = 2.5 cm

Radius of the third ball = 2.5 cm

Diameter of the third ball = 2 × r3 = 2 × 2.5 = 5 cm

Diameter of the third ball = 5 cm

Hence, the diameter of the third ball is 5 cm.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

volume of the bigger spherical ball=4/3πr^3=4/3π×27.....eq1

volume of spherical ball of radius 1.5cm=4/3π×3.375...eq2

volume of spherical ball of radius 2 cm=4/3π×8.......eq3

volume of spherical ball of radius x=4/3πx^3.....eq4

According to the question

eq1=eq2+eq3 +eq4

4/3π27=4/3π(3.375+8+x^3)

27=11.375+x^3

x^3=15.625cm^3

x=2.5cm

Radius of third spherical ball=2.5cm
Diameter=5cm

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