Question

How many cubes with edge length 1/5
In fit in a 2 2/5 x 3 1/5 x 2 prism

Answer 1

To find out how many cubes with an edge length of 1/5 can fit in a prism with dimensions 2 2/5 x 3 1/5 x 2, we calculate the volume of both the prism and the cube and then divide the prism's volume by the cube's volume. The result is that 1920 such cubes can fit inside the prism.

Step-by-step explanation:

The question asks how many cubes with an edge length of 1/5 can fit in a prism with dimensions 2 2/5 x 3 1/5 x 2. To solve this, we first convert the dimensions of the prism to an improper fraction or a whole number. This means the prism has dimensions of:

• 2 2/5 = 12/5 or 2.4 (after converting to an improper fraction)
• 3 1/5 = 16/5 or 3.2 (after converting to an improper fraction)
• 2 (this is already a whole number)

Next, we find the volume of the prism by multiplying the length, width, and height:

Volume of prism = Length × Width × Height

= (12/5) × (16/5) × 2

= (12 × 16 × 2) / (5 × 5)

= 384 / 25

= 15.36 cubic units

Then, to determine the number of small cubes that can fit in the prism, we calculate the volume of a cube with an edge length of 1/5:

Volume of cube = Edge × Edge × Edge

= (1/5) × (1/5) × (1/5)

= 1 / 125 cubic units

Finally, to find out how many such cubes can fit into the prism, we divide the volume of the prism by the volume of a cube:

Number of cubes = Volume of prism / Volume of cube

= 15.36 / (1/125)

= 15.36 × 125

= 1920

So, 1920 cubes with an edge length of 1/5 can fit in the prism.

Answer 2

96

Step-by-step explanation:

Given:

Length of edge of cube = 1/5

Measurement of prism = 2 2/5 x 3 1/5 x 2

=
`(12)/(5) * (16)/(5) *3`

Question asked :

How many cubes with edge length 1/5 fit in a prism ?

Solution:

Surface area of a cube =
`6a^(2)`

=
`6 *(1)/(5) *(1)/(5)`

=
`(6)/(25)`

Volume of prism = Lengh
`*`breadth
`*`height

=
`(12)/(5) * (16)/(5) *3`

=
`(576)/(25)`

Number of cubes fit in this prism = Volume of prism divided by Surface area of a cube

=
`(576)/(25)`
`/`
`(6)/(25)`

=
`(576)/(25)`
`*`
`(25)/(6)`

By cancelling 25 by 25 =
`(576)/(6) = 96` pieces of cubes

Thus, 96 pieces of cubes with edge length 1/5 fit in a 2 2/5 x 3 1/5 x 2 prism.