Question

A right rectangular prism has these dimensions:

Length − Fraction 1 and 1 over 4 units
Width − Fraction 5 over 8 unit
Height − Fraction 3 over 4 unit

How many unit cubes of side length Fraction 1 over 8 unit are required to pack the prism without any gap or overlap?

60
75
150
300

Answer 1

300 Launcher people huyughhfgjgfgjfgfuh

Answer 2

The unit cubes required to pack the prism without any gap or overlap are 300

Therefore, option (4) is correct.

Step-by-step explanation:

Given:

The length of a right rectangular prism $l=1\frac{1}{4}$ units = $\frac{5}{4}$ units

The width of a right rectangular prism $w =\frac{5}{8}$ units

The height of a right rectangular prism $h=\frac{3}{4}$ units

To find out:

The number of cubes of side length 1/8 units that will pack the prism

Solution:

A right rectangular prism is nothing but a cuboid

The volume of the right rectangular prism will be

$V=\frac{5}{4}\times \frac{5}{8}\times\frac{3}{4}$ unit³

$\implies V=\frac{75}{128}$ unit³

Volume of one cuboid

$=\frac{1}{8}^3$

$=\frac{1}{512}$ unit³

The number of cubes that will pack the right rectangular prism

$=\frac{75/128}{1/512}$

$=\frac{75}{128}\times 512$

$=75\times 4$

$=300$

Hope this answer is helpful,

Know More:

Q: A right rectangular prism has these dimensions:

Length: 1 1/2 units

Width: 1/2 unit

Height: 3/4 unit

How many cubes of side length 1/4 unit are required to completely pack the prism without any gap or overlap?

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