Question

Шар,обьем которого равен 21пи,вписан в куб.Найдите обьем куба С объяснениями ПОЖАЛУЙСТА!!))

Answer 1

Объем шара=4/3пR^3
объем куба в данном случае равен 8R^3
далее ищем чему равен R^3
 22п=4/3пR^3 сокращаем пи
22=4/3R^3 делим на 4/3
22*3/4=R^3
33/2=R^3 далее умножаем считаем объем куба =8*33/2=33*4=132

ответ:132

Answer 2

Finding the Volume of the Cube

To find the volume of the cube, we need to determine the length of its edges. Since the sphere is inscribed in the cube, the diameter of the sphere is equal to the length of the cube's edges.

Given that the volume of the sphere is equal to 21π, we can use the formula for the volume of a sphere to find the diameter:

Volume of a sphere = (4/3)πr^3

Since the diameter is twice the radius, we can rewrite the formula as:

Volume of a sphere = (4/3)π(d/2)^3

Simplifying the equation, we have:

21π = (4/3)π(d/2)^3

To find the diameter, we can solve for d:

(4/3)π(d/2)^3 = 21π

Dividing both sides by π and multiplying by 3/4, we get:

(d/2)^3 = 21 * (3/4)

Simplifying further:

(d/2)^3 = 63/4

Taking the cube root of both sides, we find:

d/2 = ∛(63/4)

Multiplying both sides by 2, we get:

d = 2 * ∛(63/4)

Now that we have the diameter of the sphere, we know that it is equal to the length of the cube's edges. Therefore, the volume of the cube can be calculated by cubing the length of the edges:

Volume of the cube = (d)^3

Substituting the value of d, we have:

Volume of the cube = (2 * ∛(63/4))^3

Calculating this expression will give us the volume of the cube.