How many 1-by-1-by-1-inch cubes fit inside of a rectangular prism that has a height of 4 in, width is 10 in. , and a height of 3 in.

Question

asked Oct 10, 2023 95.9k views

1 Answer

Gerardo Lima · Answer 1 · 2023-10-17T01:06:42+0000

The volume of the rectangular prism is given as

$\text{Volume(V) = Length x width x height}$

Length = 3 in

width = 10in

height = 4in

$\text{volume of the prism = 4 }*10*3=120in^3$

Volume of the 1-by-1-by-1 inch cube is

$\text{volume = length}^3$

Length =1 in

$\text{Volume of the cube = (1in)}^3=1inch^3$

The number of cubes that can fit inside the rectangular prism is hence given by

$\frac{volume\text{ of rectangular prism}}{\text{volume of cube}}$
$=(120in^3)/(1in^3)=\text{ 120 cubes}$

The answer is 120 cubes

B) The area of the prism = Length x width

Area = 3 x 10 = 30 square inch

so you will need 30 square inch of paper to cover the prism