Question

A rectangular prism is 7 cm long, 4 cm wide and 4 cm tall. How many 2 times 2 times 2 cm cubes can the prism be cut into? What is the total surface area of all the 2 times 2 times 2 times cm cubes? What is the total volume of all the 2 times 2 times 2 times cm cubes. Plz I will give you 100 points

Answer 1

Answer: The number of 2 times 2 times 2 cm cubes is 14. The total surface area of all the 2 times 2 times 2 times cm cubes is 336 cm square. The total volume of all the 2 times 2 times 2 times cm cubes is 112 cm cube.

Step-by-step explanation:

It is given that the A rectangular prism is 7 cm long, 4 cm wide and 4 cm tall.

The volume of rectangular prism is,

`V_1=l* b* h`

`V_1=7* 4* 4`

`V_1=112`

Therefore, the volume of rectangular prism is 112 cm square.

The volume of cubes is,

`V_2=a^3`

`V_2=(2)^3`

`V_2=8`

The number of cubes in the rectangular prism is,

`N=(V_1)/(V_2) =(112)/(8) =14`

Therefore, the number of cubes is 14.

Total surface area of a cube is,

`A=6a^2`

`A=6(2)^2`

`A=24`

Total surface area of all cubes is,

`14* A=14* 24=336`

Therefore the total surface area of all cubes is 336 cm square.

Total volume of all cubes is equal t the volume of rectangular prism, i.e, 112 cm cube.