We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
236
5
avatar+95 

It is known that a cube is inscribed in a sphere. If the volume of the cube is 30, what is the volume of the sphere?

 Sep 9, 2018
 #1
avatar+18457 
0

Oooops..... read that backwards.......I'll be back shortly

 Sep 9, 2018
edited by ElectricPavlov  Sep 9, 2018
 #2
avatar+95 
+1

Please answer ASAP.

 Sep 9, 2018
 #3
avatar+18457 
+2

Volume of a cube = lxlxl       l^3 = 30         so the sides of the cube are = 3.10723 units

 

From the CENTER of the cube to one of its corners is the radius of the SPHERE

       The Corner - to - corner diagonal thru-the-center distance of the cube is   sqrt( l^2 + l^2 + l^2) = 5.3818 units

               so the center to the corner is 1/2 of this   or   2.6909 units = radius of SPHERE

 

VOLUME of SPHERE = 4/3 x pi x r^3

                                    = 4/3 x pi x 2.6909^3 = 81.62 units^3

 Sep 9, 2018
edited by ElectricPavlov  Sep 9, 2018
 #4
avatar+95 
+1

Thank You for your detailed answer.

hellospeedmind  Sep 9, 2018
 #5
avatar+18457 
+1

You're welcome, as always!  cheeky

ElectricPavlov  Sep 9, 2018

12 Online Users

avatar
avatar