Sphere

My first math answer for this year:)

Take the cuberoot of the cube volume to get the side length.

\(\sqrt[3]{1000} = 10\)

Diagonal of a cube is

\(s*\sqrt{3} = d\\ 10*\sqrt{3} = 17.32 \)

That is equal to the diameter of the sphere

Now take half that for the radius

\(\dfrac{17.32}{2} = 8.66\)

Then the volume of the the sphere is

\(\dfrac{4}{3}\pi * 8.66^3 = 2720.5 ~ units \)

So the smallest sphere that will hold a cube of 1000 is 2720.5 units

i found thanks ! (250pi sqrt(2)

Actually this is a really good 3 dimensional question !

Some of our members may like to have a go at it!  

So long as you know how to find the volume of a sphere   V=(4/3) pi*r^3

and the volume of a cube  then you can try it !!

HINT: You may need to use the Pythagorean Theorem too!

Excellent answer Dragonlance but don't forget your units.

I know there are none in the question but you should add units and units³  anyway   

Excellent thinking, Dragonlance.......!!!!!

Here's a pic of the cross-section of the cube within the sphere showing that Dragonlance's answer is indeed correct.....!!!

Thanks Chris, 

This is a clip to show you how to find the legth of the diagonal of the cube

https://www.youtube.com/watch?v=UN8wB0KdmiQ