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?

Mellie
Apr 21, 2017

#1**+5 **

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

Do you see what to do now?

If you need more help please just ask :)

hectictar
Apr 21, 2017