Question

Сравни объёмы и площади поверхностей куба и прямоугольного параллелепипеда если ребро куба равно 5 дм а измерения прямоугольного параллелепипеда 15 см 1м и 8 дм

Answer 1

Sкуба=а^2=25дм^2
Sпар.=a*b=1.5*10=15дм^2
Vкуба=a^3=5^3=125дм^3
Vпар=a*b*c=1.5*10*8=120дм^3

Answer 2

Comparing the Volumes and Surface Areas of a Cube and a Rectangular Parallelepiped

To compare the volumes and surface areas of a cube and a rectangular parallelepiped, we'll first calculate the values for each shape based on the given dimensions.

Given Dimensions: - Cube: Side length = 5 dm - Rectangular Parallelepiped: Length = 1 m, Width = 15 cm, Height = 8 dm

Calculating the Volume and Surface Area of a Cube

The volume of a cube is given by the formula V = a^3, where a is the length of a side.

The surface area of a cube is given by the formula A = 6a^2, where a is the length of a side.

Using the given side length of the cube (5 dm), we can calculate the volume and surface area of the cube.

Volume of the Cube: V = 5^3 = 125 dm^3

Surface Area of the Cube: A = 6 * 5^2 = 150 dm^2

Calculating the Volume and Surface Area of a Rectangular Parallelepiped

The volume of a rectangular parallelepiped is given by the formula V = l * w * h, where l, w, and h are the length, width, and height, respectively.

The surface area of a rectangular parallelepiped can be calculated using the formula A = 2lw + 2lh + 2wh.

Using the given dimensions of the rectangular parallelepiped (1 m, 15 cm, 8 dm), we can calculate the volume and surface area.

Converting Dimensions to Decimeters: - Length: 1 m = 10 dm - Width: 15 cm = 1.5 dm - Height: 8 dm (already in dm)

Volume of the Rectangular Parallelepiped: V = 10 * 1.5 * 8 = 120 dm^3

Surface Area of the Rectangular Parallelepiped: A = 2(10*1.5 + 10*8 + 1.5*8) = 2(15 + 80 + 12) = 2(107) = 214 dm^2

Comparison of Volumes and Surface Areas

- Volume: - The volume of the cube is 125 dm^3, while the volume of the rectangular parallelepiped is 120 dm^3. - Surface Area: - The surface area of the cube is 150 dm^2, while the surface area of the rectangular parallelepiped is 214 dm^2.

In summary, the cube has a greater volume (125 dm^3) compared to the rectangular parallelepiped (120 dm^3), but the rectangular parallelepiped has a larger surface area (214 dm^2) compared to the cube (150 dm^2).

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