Equation of the sphere with centre (2,3,7) and radius 10 in R3⟹(x−2)2+(y−3)2+(z−7)2=102
Thus, extremities of the sphere in all 3 directions can be found as :
∣x−2∣<10,∣y−3∣<10,∣z−7∣<10 .
But the given cube is P={(x,y,z):∣x−2∣<11,∣y−3∣<11,∣z−7∣<11}
Thus, clearly the sphere lies inside the cube as its extremities are smaller than extremities of the cube!
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