Question

A rectangular prism is 8 cm long, 4 cm wide and 4 cm tall how many 2 times 2 times 2 can the prism be cut into.What is the total surface area of all the 2 times 2 times 2 cubes.What is the total volume of all the 2 times 2 times 2 cm cubes

Answer 1

The number of cubes is which can the rectangular prism be cut into is 16.

Therefore total surface area of the all cubes is 384 cm².

The volume of all cubes is 128 cubic cm.

Explanation:

Given that,

a rectangular prism is 8 cm long, 4 cm wide and 4 cm tall.

The dimensions of a cube is 2 cm × 2 cm × 2 cm.

Since the cubes cuts out from the rectangular prism.

So the volume of the rectangular prism= the volume of the cubes.

Let the number of cubes which cut out from the rectangular prism be x.

The volume of the rectangular prism is = (8×4×4) cubic cm

The volume of x cubes is =x (2×2×2)cubic cm

According to the problem,

x (2×2×2)=8×4×4

`\Rightarrow x=(8* 4* 4)/(2*2*2)`

`\Rightarrow x=16`

The number of cubes is which can the rectangular prism be cut into is 16.

The surface area of a cube is = 6× side²

Each sides of the cube are 2 cm.

The surface area of 16 cubes is =( 16×6×2²) cm²

=384 cm²

Therefore total surface area of the all cubes is 384 cm².

Since the volume of the rectangular prism= the volume of the cubes.

The volume of the rectangular prism is = (8×4×4) cubic cm

=128 cubic cm

The volume of all cubes is 128 cubic cm.