Answer:
6.6 inch
Explanation:
If the diameter of the solid balls are 2 inches, 4 inches and 6 inches respectively.
Recall that:
Radius=Diameter/2
It means the radii of the balls are 1 inch, 2 inch and 3 inch respectively.
To find the approximate diameter of the new ball, we find first the combined volume of the three balls.
Volume of a Sphere=⁴/₃πr³
Combined Volume of the Three balls=Volume of Ball with radius 1 + Volume of Ball with Radius 2 + Volume of Ball with Radius 3.
=⁴/₃πr³+⁴/₃πr³+⁴/₃πr³
=⁴/₃π(1³+2³+3³)
=⁴/₃π(1+8+27)
=⁴/₃π X 36
= 48π
Volume of the new ball = 48π
Next, we determine its diameter,
⁴/₃πr³=48π
Dividing both sides by π
⁴/₃r³=48
r³=48X(3/4)
r³=36
Take the cube root of both sides
r=3.30192724889= 3.3 inch
Now Diameter= Radius X 2
Approximate Diameter of the new ball =3.3 X 2
=6.6 inch