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.

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,

$V_1=l\times b\times h$

$V_1=7\times 4\times 4$

$V_1=112$

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,

$N=\frac{V_1}{V_2} =\frac{112}{8} =14$

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,

$14\times A=14\times 24=336$

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.