Question

27. Дана длина ребра куба a. Найдите объем куба (v = a?) и площадь его поверхности (s = ба?).

Answer 1

Ответ:

V = a³, S = 6а².

Объяснение:

а - длина ребра куба, тогда его объём равен V = a³, а площадь поверхности состоит из площади шести равных граней, каждая из которых квадрат со стороной а, поэтому

S поверхности куба = 6а².

Answer 2

Calculation of the Cube's Volume and Surface Area

To find the volume and surface area of a cube, we need to know the length of one of its edges, denoted as 'a'.

Volume of a Cube (V): The volume of a cube is calculated by raising the length of one of its edges to the power of 3. Therefore, the formula for the volume of a cube is:

V = a^3.

Surface Area of a Cube (S): The surface area of a cube is calculated by multiplying the length of one of its edges by itself and then multiplying the result by 6. Therefore, the formula for the surface area of a cube is:

S = 6a^2.

Now, let's calculate the volume and surface area of the cube with the given edge length 'a = 27'.

Volume of the Cube (V): Substituting the value of 'a' into the formula for the volume of a cube, we have:

V = 27^3 = 19683 cubic units.

Therefore, the volume of the cube is 19683 cubic units.

Surface Area of the Cube (S): Substituting the value of 'a' into the formula for the surface area of a cube, we have:

S = 6 * 27^2 = 1458 square units.

Therefore, the surface area of the cube is 1458 square units.

In summary, for a cube with an edge length of 27 units, the volume is 19683 cubic units, and the surface area is 1458 square units.