Question

Войдет ли куб с длинной общей всех ребер равной 120 мм в шар с радиусом 8мм

Answer 1

Находишь длину диагонали куба. Если найденное значение больше диаметра шара, то не войдёт, а если меньше - войдёт.
Диаметр: 16(мм)
Если имеется ввиду, что 120 - это сумма длин всех рёбер куба, то:
120:12 = 10(мм) - длина ребра
d=√(a²+a²) = √(2a²), где d - диагональ грани куба, а - ребро куба
D = √(d²+a²) = √(3a²) = 10√3(мм) , где D - диагональ куба.

10√3 > 16
⇒Не войдёт

Answer 2

Checking if a Cube Can Fit Inside a Sphere

To determine if a cube with a total edge length of 120 mm can fit inside a sphere with a radius of 8 mm, we can use the relationship between the diagonal of the cube and the diameter of the sphere.

The diagonal of a cube can be calculated using the formula: Diagonal = √3 * edge length

The diameter of the sphere is twice the radius: Diameter = 2 * radius

Let's calculate the diagonal of the cube and the diameter of the sphere to see if the cube can fit inside the sphere.

Calculations

The diagonal of the cube: Diagonal = √3 * 120 mm

The diameter of the sphere: Diameter = 2 * 8 mm

Results

The diagonal of the cube is calculated to be approximately 207.85 mm, and the diameter of the sphere is 16 mm.

The diagonal of the cube (207.85 mm) is greater than the diameter of the sphere (16 mm), so the cube cannot fit inside the sphere.

This conclusion is based on the calculations of the diagonal of the cube and the diameter of the sphere, which indicate that the cube is too large to fit inside the given sphere.

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