Answer:
The volume of the rectangular prism is 243 cm³
Step-by-step 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
Answer:
The volume of the rectangular prism is 243 cm³.
Step-by-step explanation:
It is given that the area of the top faces of a cube is 9 square centimeters.
The area of a square is
[tex]A=a^2[/tex]
Substitute A=9 to find the edge of the cube.
[tex]9=a^2[/tex]
Taking square root both sides.
[tex]\sqrt{9}=a[/tex]
[tex]3=a[/tex]
The edge of the cube is 3 cm.
The volume of a cube is
[tex]V=a^3[/tex]
The volume of cube is
[tex]V=(3)^3=27[/tex]
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
[tex]V=9\times (\text{Volume of a cube})[/tex]
[tex]V=9\times 27[/tex]
[tex]V=243[/tex]
Therefore the volume of the rectangular prism is 243 cm³.
