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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?

hellospeedmind  Sep 9, 2018
 #1
avatar+12727 
0

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

ElectricPavlov  Sep 9, 2018
edited by ElectricPavlov  Sep 9, 2018
 #2
avatar+21 
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Please answer ASAP.

hellospeedmind  Sep 9, 2018
 #3
avatar+12727 
+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

ElectricPavlov  Sep 9, 2018
edited by ElectricPavlov  Sep 9, 2018
 #4
avatar+21 
+1

Thank You for your detailed answer.

hellospeedmind  Sep 9, 2018
 #5
avatar+12727 
+1

You're welcome, as always!  cheeky

ElectricPavlov  Sep 9, 2018

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