Question

Find the length of the diagonal of a cube that can be inscribed in a sphere of radius 9 cm?

Answer 1

Answer:

magine the cube inside the hemisphere.

Then there are four vertices touching the "dome", and four lying on the "floor".

Consider the plane going through two opposite vertices (each) of the squares defined by the upper and lower planes of the cube.

You have then defined a rectangle of height a

, being the side of the cube, and of length 2–√a

, being the diagonal of the square.

You know that the distance between the center of the sphere and any upper vertex is 42–√

. But this is also the hypothenuse of the triangle defined by the center of the sphere, and two vertices of the said rectangle.

Thus a2+(2–√a2)2=42–√

and a=83–√

The diagonal is indeed 3–√a

, that is, 8cm.

Step-by-step explanation: