+1836 What is the volume of the largest ball that can be packed into a cubic cardboard box whose edges have length a. 1 foot? b. 2 feet? c. 3 feet?
+9481 The diameter of the largest ball that can fit in a cube matches the length of the cube's edge.
volume of a sphere = \(\frac43 * \pi * \text{radius}^3\)
a.
diameter = 1 , radius = 1/2
volume = \(\frac43*\pi*(\frac12)^3=\frac{\pi}6 \approx 0.524 \text{ cubic feet}\)
b.
diameter = 2 , radius = 1
volume = \(\frac43 * \pi * 1^3 = \frac{4\pi}{3} \approx 4.189 \text{ cubic feet}\)
c.
diameter = 3 , radius = 3/2
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