How many times is the surface area of a ball described about a cube greater than the surface area
| July 30, 2021 | education
How many times is the surface area of a ball described about a cube greater than the surface area of a ball inscribed in the same cube?
If the ball is described around a cube, then its radius is half the diagonal:
D = a√3;
R = a√3 / 2.
If the ball is inscribed in a cube, then its radius is half the edge:
r = a / 2;
Sп = 4π (number pi 3.14) R ^ 2.
The area ratio is the ratio of the squares of the radii:
R ^ 2 / r ^ 2 = 3.
Answer: 3 times the surface area of a ball described about a cube is greater than the surface area of a ball inscribed in the same cube.
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