+0  
 
0
883
2
avatar+1760 

A spherical holiday ornament with a radius r is to be packacked in a cubical box so that all sides touch the sphere. What is the ratio of the volume of the sphere to the volume of the cube? If the same ornament in the problem above is to be packed in a cylinder so that all surfaces touch the sphere, what is the ratio of the volume of the sphere to the volume of the cylinder?

Mellie  Apr 21, 2017
Sort: 

2+0 Answers

 #1
avatar+76912 
+4

Good to see you, Mellie....!!!

 

V cube  =   s^3        where s is the side length of the cube   (1)

V sphere in a cube   =  (4/3)pi (1/2s)^3    (2)

 

Ratio  of  (2)  to (1)   =

 

(4/3)pi (1/2s)^3 /  s^3   =

 

(4/3)pi *(1/8)s^3 /s^3 

 

(4/3)pi (1/8) / 1  =

 

pi / 6

 

 

 

V cylinder  =   pi * r^2 * h  →  pi*r^2 *(2 r )  → 2* pi*r^3  (1)

V sphere  =   (4/3) * pi * r^3    (2)

 

Ratio  of  (2)  to (1)  =

 

[(4/3) pi * r^3 ] / [ 2 *pi * r^3 ]  =

 

(4/3) /  2  =

 

4/6  =

 

2/3

 

 

 

cool cool cool

CPhill  Apr 21, 2017
 #2
avatar+1760 
+1

HI!!! I haven't been here in a while. It's good to see you too! Thank you so much for all your help!

Mellie  Apr 21, 2017

20 Online Users

avatar
avatar
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