Question

Длина прямоугольного параллелепипеда равна 90 см, ширина 25 см, а высота 12 см. Найти длину ребра куба, объём которого равен объёму этого прямоугольного параллелепипеда. У какой из двух фигур площадь поверхности больше и на сколько?

Answer 1

1 ) 90 * 25 * 12 = 27000 см3
2 ) 27000 = 30 * 30 * 30 см  ребро куба 
3)  25 * 90 = 2250 cм 2
4) 30 * 30 = 900 cм 2
5) 2250  больше 900  
              то есть у параллилепипеда S поверхности больше 

Answer 2

Calculation of Cube Edge Length and Volume

To find the length of the edge of a cube with the same volume as the given rectangular parallelepiped, we can use the formula for the volume of a cube, which is equal to the length of one of its edges cubed.

The volume of the rectangular parallelepiped is given by the formula V = length × width × height. In this case, the length is 90 cm, the width is 25 cm, and the height is 12 cm.

Substituting the given values into the formula, we have:

V = 90 cm × 25 cm × 12 cm

To find the length of the edge of the cube, we need to find the cube root of the volume. Let's calculate the volume first:

V = 27000 cm³

Now, let's find the cube root of the volume to determine the length of the edge of the cube:

Cube Edge Length: The cube root of 27000 cm³ is approximately 30 cm.

Therefore, the length of the edge of the cube, which has the same volume as the given rectangular parallelepiped, is approximately 30 cm.

Comparison of Surface Areas

To determine which of the two figures has a larger surface area, we need to calculate the surface area of each figure.

Surface Area of the Rectangular Parallelepiped: The surface area of a rectangular parallelepiped can be calculated using the formula S = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

Substituting the given values into the formula, we have:

S = 2(90 cm × 25 cm) + 2(90 cm × 12 cm) + 2(25 cm × 12 cm)

Simplifying the equation, we get:

S = 4500 cm² + 2160 cm² + 600 cm²

S = 7260 cm²

Surface Area of the Cube: The surface area of a cube can be calculated using the formula S = 6a², where a is the length of one of its edges.

Substituting the value we found earlier for the length of the edge of the cube, we have:

S = 6(30 cm)²

Simplifying the equation, we get:

S = 6 × 900 cm²

S = 5400 cm²

Comparing the surface areas, we find that the surface area of the rectangular parallelepiped is 7260 cm², while the surface area of the cube is 5400 cm².

Therefore, the surface area of the rectangular parallelepiped is larger than the surface area of the cube by 1860 cm².

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