Question

Шар, объём которого равен 6 пи вписан в куб. Найдите объём куба.

Answer 1

Из формулы объема шара V = 4/3 $\pi R^3$, выражаем $R^3$ = 3V/4$\pi$ = 4,5
ребро куба = диаметру шара
V куба = $d^3 = (2R)^3 = 8R^3$ = 4,5*8 = 36

Answer 2

Calculation of the Cube's Volume

To find the volume of the cube, we need to determine the length of its sides. Given that the volume of the sphere inscribed in the cube is equal to 6π, we can use this information to calculate the volume of the cube.

Let's denote the length of the side of the cube as s.

The volume of a cube is given by the formula: V = s^3.

Since the sphere's volume is equal to 6π, we have the equation: 6π = s^3.

To find the value of s, we can take the cube root of both sides of the equation:

∛(6π) = ∛(s^3).

Therefore, the length of the side of the cube is equal to the cube root of 6π.

Now, let's calculate the volume of the cube using the obtained value of s.

Calculation Steps:

1. Calculate the cube root of 6π: ∛(6π). 2. Cube the result obtained in step 1 to find the volume of the cube: V = (∛(6π))^3.

Let's perform the calculations:

1. Cube root of 6π: - ∛(6π) ≈ 1.81712059283.

2. Volume of the cube: - V = (∛(6π))^3 ≈ (1.81712059283)^3 ≈ 6π.

Therefore, the volume of the cube is approximately equal to 6π.

Please note that the exact numerical value of the volume depends on the precise value of π used in the calculations.

I hope this helps! Let me know if you have any further questions.