Q
QuestionMathematics

Calculate the total number of gumballs that need to fit in the machine if each gumball has a diameter of 1.25 inches.
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Answer

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Step 1
: First, we need to find the volume of a single gumball.

r = \frac{1.25 \text{ inches}}{2} = 0.625 \text{ inches}
Since a gumball is a sphere, we can use the formula for the volume of a sphere: Since the diameter is 1.25 inches, the radius is half of that:

Step 2
: Now, substitute the value of the radius into the formula for the volume of a sphere:

V_{gumball} = \frac{4}{3} \pi (0.625 \text{ inches})^{3}

Final Answer

Approximately 20497 gumballs can fit in the gumball machine, assuming the machine has a cylindrical gumball compartment with a height of 30 inches and a diameter of 10 inches.