Question

the area of the top faces of a cube is 9 square centimeters. Use 9 of these cubes to make a rectangular prism. what is the voulme of the rectangular prism

Answer 1

The volume of the rectangular prism is 243 cm³.

Explanation:

It is given that the area of the top faces of a cube is 9 square centimeters.

The area of a square is

`A=a^2`

Substitute A=9 to find the edge of the cube.

`9=a^2`

Taking square root both sides.

`√(9)=a`

`3=a`

The edge of the cube is 3 cm.

The volume of a cube is

`V=a^3`

The volume of cube is

`V=(3)^3=27`

The volume of a cube is 27 cm³.

It is given that 9 of these cubes are used to make a rectangular prism.

The volume of the rectangular prism is

`V=9* (\text{Volume of a cube})`

`V=9* 27`

`V=243`

Therefore the volume of the rectangular prism is 243 cm³.

Answer 2

The volume of the rectangular prism is 243 cm³

Explanation:

* Lets explain how to solve the problem

- The top face of the cube has an area of 9 cm²

∵ All the faces of the cube are squares

∴ The top face is a square

∵ Area of any square = L² , where L is the length of the side of

the square

∵ Area of the top face is 9 cm²

∴ L² = 9 ⇒ take √ for both sides

∴ L = 3 cm

∵ The volume of any cube = L³

∵ L = 3 cm

∴ The volume of the cube = (3)³ = 27 cm³

- We will use 9 cubes to make a rectangle prism

∴ The volume of the rectangle prism is equal to the volume of

the 9 cubes

∴ The volume of the prism = 9 × volume of a cube

∵ The volume of the cube is 27 cm³

∴ The volume of the prism = 9 × 27 = 243 cm³

* The volume of the rectangular prism is 243 cm³