For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is 4 3 πr3

6.6 inch

Step-by-step 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