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27 October, 12:37

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

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  1. 27 October, 15:27
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    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
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