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# Can someone help me through this?: A cube with edges 6 inches long fits snugly inside a sphere. The diagonal of the cube is the diameter of the sphere. What is the volume, to the nearest whole number, of the space between the sphere and the cube?

to find the diameter of the sphere you have to find the diagonal of the cube by using the Pythagoras theorem twice. the first time is to find out the diagonal length of the base of the cube. sqrt(6^2 +6^2)=sqrt(72) with this new information we can now find out the diagonal of the cube (diameter of the sphere) sqrt(6^2 +(sqrt(72))^2) =sqrt(36+72) =sqrt(108) =6root3 to fInd the volume of a sphere you have to use the formula: 4/3(pi)(r^3) since the diameter is 6root3 the radius must be 3root3 4/3(pi)(3root3)^3=587.670994 the volume of the cube Is just 6^3=216 the space between the sphere and the cube is: 587.670994-216 =371.67 =372 inches^3 (to the nearest whole number)  Samantha Rajaratnam
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Maths

6(1/2)^n-1

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