Question

find the diameter of sphere which contain a cube of side a cm side

Answer 1

Since the sphere is touching the sides of the cube, the diameter of the sphere will be equal to the length of one side of the cube. The side of the cube 's' is given to be 4 cm.

Therefore diameter d = 4 cm

Therefore radius r = d/2 = 2 cm

Since the Gap is the space remaining after the sphere occupies it's position in the cube, the volume of the gap (say G) will be the same as the volume of the sphere (say S) taken out from the volume of the cube (say C). I.e G = C - S

Now the volume of a cube is given by V = (s ^ 3) where 's' is the length of the side of the cube (remember all sides of the cube have same length)

Therefore C = (4 ^ 3) = 64 cu cm.

Also volume of a sphere is given by V = (4/3) * π * (r ^ 3) where 'r' is the radius of the sphere.

Now r = 2 cm and π is approximately 3.14

So S = (4/3) * π * (2 ^ 3) = (4 * 3.14 * 8)/3 = 100.48/3 = 33.4933 cu cm.

So finally G = C - S = 64 - 33.4933 = 30.5067 cu cm.

So the volume of the gap is approximately 30.51 cu cm.

Answer 2

Answer:

Step-by-step explanation:

AB,BC,CD,AD are the sides of a cube . And AC is the diagonal so by pythagorus theorem we can find it

AC^2=AB^2+BC^2

AC^2=a^2+a^2

AC^2=2a^2

AC=√2a^2

hope it is helpful.............