A rectangle prism is 8 cm long. a)How many 2 x 2 x 2 cm cubes can the prim be cut into? b)What is the total surface area of all the 2 x 2 x 2 cm cubes? c) What is the total volume of all the 2 x 2 x 2 cubes?
Prism* I meant.
You only give the length. What about the other two dimensions?
Anyway, just figure out how many 2" sides fit into the various dimensions, then multiply those 3 numbers to get the number of 2" cubes.
Each 2" cube has a surface of 6(2*2)=24 cm^2
Each small cube has a volume of 2^3 = 8 cm^3
a) To find out how many 2 x 2 x 2 cm cubes can fit into the rectangular prism, we need to divide the length of the prism by the length of one side of the cube.
In this case, the rectangular prism is 8 cm long, and the cube's side length is 2 cm. So, we divide 8 by 2:
8 cm ÷ 2 cm = 4
Therefore, the rectangular prism can be cut into 4 of the 2 x 2 x 2 cm cubes.
b) To determine the total surface area of all the cubes, we need to calculate the surface area of one cube and then multiply it by the total number of cubes.
The surface area of a cube is given by the formula: 6s^2, where s is the side length of the cube. In this case, s is 2 cm.
Surface area of one cube = 6 x (2 cm)^2 = 6 x 4 cm^2 = 24 cm^2
Since we have 4 cubes, we can multiply the surface area of one cube by 4:
Total surface area = 24 cm^2 x 4 = 96 cm^2
Therefore, the total surface area of all the 2 x 2 x 2 cm cubes is 96 cm^2.
c) To calculate the total volume of all the 2 x 2 x 2 cm cubes, we need to calculate the volume of one cube and then multiply it by the total number of cubes.
The volume of a cube is given by the formula: s^3, where s is the side length of the cube. In this case, s is 2 cm.
Volume of one cube = (2 cm)^3 = 2 cm x 2 cm x 2 cm = 8 cm^3
Since we have 4 cubes, we can multiply the volume of one cube by 4:
Total volume = 8 cm^3 x 4 = 32 cm^3
Therefore, the total volume of all the 2 x 2 x 2 cm cubes is 32 cm^3.