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Volume

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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
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#1
+4711
+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?

hectictar  Apr 21, 2017
#2
+1760
+3

Oh yeah! Thank you!!! I really appreciate your help! :)

Mellie  Apr 21, 2017
#3
+4711
+4

No prob! Thanks!

hectictar  Apr 21, 2017

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