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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
 #1
avatar+7336 
+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
 #2
avatar+1794 
+3

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

Mellie  Apr 21, 2017
 #3
avatar+7336 
+4

No prob! Thanks! smiley

hectictar  Apr 21, 2017

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