Question

A large rectangular prism has a length of 2 and 1/2 inches, a width of 4 inches, and a height of 1 and 1/2 inches. A smaller cube has a length, width, and height of 1/2 of an inch. How many of the smaller cubes will fit into the larger rectangular prism?

Answer 1

120 cubes

Explanation:

Volume of prism and cube:

We can find the number of smaller cubes that will fit into larger rectangular prism by dividing the volume of prism by the volume of cube.

Rectangular prism:

`\sf l = 2(1)/(2) =(5)/(2) \ inches\\\\w = 4 \ inches\\\\h =1(1)/(2)=(3)/(2) \ inches\\`

`\sf \boxed{\text{\bf Volume of rectangular prism= l * w * h}}`

`\sf =(5)/(2)*4*(3)/(2)\\\\= 5*1*3\\\\= 15 \ in^3`

Cube:

`\sf side = (1)/(2) \ inches\\`

`\sf \boxed{\text{ \bf Volume of cube = side * side *side}}`

`\sf =(1)/(2)*(1)/(2)*(1)/(2)\\\\ =(1)/(8) \ in^3`

Number of cubes = Volume of prism ÷ volume of a cube

`\sf = 15 / \ (1)/(8)\\\\=15 *(8)/(1)\\\\= 120`

120 cubes will fit