Find the square of the diameter of a sphere circumscribed about a cube whose edge is 1.
| August 16, 2021 | education
The diameter of a circle circumscribed about a cube is the diagonal BC of this cube.
All the faces of the cube are squares. We construct a diagonal AC at the base of the cube, then by the Pythagorean theorem, AC ^ 2 = AD ^ 2 + CD ^ 2 = 1 + 1 = 2.
AC = √2 cm.
In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse BC.
BC ^ 2 = AB ^ 2 + AC ^ 2 = 1 + 2 = 3.
D ^ 2 = 3.
Answer: The square of the diameter of the sphere is 3.
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