Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant.  The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

Volume =

Maximize volume subject to

i.e.

Use Lagrangian multipliers , we have

at the maximum

Dividing we get

Similarly

Thus we get

Hence dimensions are

(2x,2y,2z)

So dimensions are

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step-by-step explanation:

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the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.