+0  
 
0
195
3
avatar+1766 

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
Sort: 

3+0 Answers

 #1
avatar+5541 
+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+1766 
+3

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

Mellie  Apr 21, 2017
 #3
avatar+5541 
+4

No prob! Thanks! smiley

hectictar  Apr 21, 2017

19 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details