Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 4.6 AIME Find the answer United States

Problem:

Patrick and Anderson are having a snowball fight. Patrick throws a snowball at Anderson which is shaped like a sphere with a radius of $10$ centimeters. Anderson catches the snowball and uses the snow from the snowball to construct snowballs with radii of $4$ centimeters. Given that the total volume of the snowballs that Anderson constructs cannot exceed the volume of the snowball that Patrick threw, how many snowballs can Anderson construct?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

$\left\lfloor\left(\frac{10}{4}\right)^3\right\rfloor = \left\lfloor\frac{125}{8}\right\rfloor = 15.$

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