A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of the two of the balls are 1.5 cm and 2 cm respectively. Determine the diameter of the third ball.
Answers
Answer:
The diameter of the third ball is 5 cm.
SOLUTION :
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...
According to the question
Radius of the spherical ball=3cm
We know that the volume of the sphere= 43Πr3
So it’s volume (v)= 43Πr3
Given that,
That the ball is melted and recast into 3
spherical balls.
Volume (V1) of first ball = 43∏1.53
Volume (V2) of second ball = 43∏23
Radii of the third ball be =r cm
Volume of third ball (V3) = 43∏r3
Volume of the spherical ball is equal to the volume of the 3 small spherical balls.
V=V1+V2+V3
43Πr3= 43∏1.53+ 43∏+23+ 43∏r3
Now,
Cancelling out the common part from both sides of the equation we get,
(3)³= (2)³ +(1.5)³+r³
r³=3³-2³-1.5³ cm³
r³=15.6cm³
r= (15.6)⅓ cm
r=2.5cm
we know that diameter = 2* radius
=2*2.5 cm
=5.0 cm
The diameter of the third ball is 5.0 cm
Hope its help you