reginah asked in Science & MathematicsMathematics · 1 decade ago

Find the volume of the largest cube contained the sphere? given: radius = 3cm.?

pls. can u help me? :((

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• 1 decade ago

The radius of the sphere = the distance from the centre of the cube to a corner.

let 'x' be the length of one side of the cube

the distance from the centre of a face to the corner = x/√2

therefore the distance from the centre of the cube to a corner

= (x/√2)^2 + (x/2)^2 all square rooted

= √(3x^2/4)

the radius is 3cm

3 = √(3x^2/4)

9 = 3x^2/4

36 = 3x^2

x = √12

The volume is 12√12 = 24√3 cm^3

or approximately 41.57cm^3

• 1 decade ago

if you consider a single view of that sphere, the largest square contained in that is the one whose diagonal is equal to the diameter of the circle.

so the diagonal of the square is 6 cm.

so, side^2+side^2 = diagonal^2

2 Side^2 = 36

side = 3√2

so the largest cube contained in the sphere is same as the largest square in the circle,

so cube side is 3√2, so volume = (3√2)^3 = 54√2 = 76.367 cm^3