Question

Дана правильная четырёхугольная призма со стороной основания 9 см. Высота призмы равна 27 см. Определите, чему равно ребро куба, объём которого совпадает с объёмом этой призмы.

Answer 1

Ответ:

9*³√3 см

Объяснение:

Sосн=а²; где а=9см

Sосн=9²=81см² площадь основания призмы.

Vпр=Sосн*h; где h=27см

Vпр=81*27=2187 см³ объем призмы.

Vпр=Vк

Vк=2187см³

Vк=с³; где с- ребро куба

с=³√Vк=³√2187=9*³√3 см

Answer 2

Calculating the Edge Length of the Cube

To determine the edge length of the cube whose volume is equal to the volume of the given prism, we can use the formula for the volume of a cube, which is V = a^3, where "a" represents the edge length of the cube.

The volume of the given prism can be calculated using the formula V = base area * height. The base area of a rectangular prism is given by the formula base area = length * width. In this case, the base area is 9 cm * 9 cm, and the height is 27 cm.

Let's calculate the volume of the prism and then find the edge length of the cube.

Calculation

The volume of the prism is given by V = base area * height. Substituting the values, we get:

V = 9 cm * 9 cm * 27 cm = 2187 cm^3.

Now, to find the edge length of the cube, we use the formula V = a^3, where V is the volume of the cube and "a" is the edge length.

So, a^3 = 2187 cm^3.

Taking the cube root of both sides, we find:

a = 12 cm.

The edge length of the cube, whose volume is equal to the volume of the given prism, is 12 cm.