Question

Ширина прямоугольника параелепипеда равна 3 см высота 2 см а площадь передней грани 12 см в кубе вычесли его объём и площадь омтальных граней

Answer 1

Ширина 3 см
высота 2см
передняя грань 12 см кв = длина*высота
12=длина*2
значит длина 6см
объем = длина*ширина*высота=6*3*2=36 см куб
боковая грань = ширина*высота=3*2=6 см кв
верхняя\нижняя грань=длина*ширина=6*3=18 см кв

Answer 2

Calculating the Volume and Total Surface Area of a Rectangular Parallelepiped

To calculate the volume and total surface area of a rectangular parallelepiped, we can use the given dimensions and the formulae for volume and surface area.

Given: - Width of the rectangular parallelepiped = 3 cm - Height of the rectangular parallelepiped = 2 cm - Area of the front face = 12 cm²

Calculating the Volume

The volume of a rectangular parallelepiped can be calculated using the formula: \[ \text{Volume} = \text{Width} \times \text{Height} \times \text{Depth} \]

Substituting the given values: \[ \text{Volume} = 3 \, \text{cm} \times 2 \, \text{cm} \times \text{Depth} \]

To find the depth, we can use the given area of the front face.

From Source we have: \[ 12 = 3 \times 2 \times \text{Depth} \] \[ \text{Depth} = \frac{12}{6} = 2 \, \text{cm} \]

Therefore, the volume of the rectangular parallelepiped is: \[ \text{Volume} = 3 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm} = 12 \, \text{cm}^3 \]

Calculating the Total Surface Area

The total surface area of a rectangular parallelepiped can be calculated using the formula: \[ \text{Total Surface Area} = 2 \times (\text{Width} \times \text{Height} + \text{Height} \times \text{Depth} + \text{Width} \times \text{Depth}) \]

Substituting the given values: \[ \text{Total Surface Area} = 2 \times (3 \, \text{cm} \times 2 \, \text{cm} + 2 \, \text{cm} \times 2 \, \text{cm} + 3 \, \text{cm} \times 2 \, \text{cm}) \] \[ \text{Total Surface Area} = 2 \times (6 \, \text{cm}^2 + 4 \, \text{cm}^2 + 6 \, \text{cm}^2) \] \[ \text{Total Surface Area} = 2 \times 16 \, \text{cm}^2 = 32 \, \text{cm}^2 \]

Conclusion

Therefore, the volume of the rectangular parallelepiped is 12 cm³ and the total surface area is 32 cm².