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

Answer:

120 cubes

Step-by-step 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:

       $\sf l = 2\dfrac{1}{2} =\dfrac{5}{2} \ inches\\\\w = 4 \ inches\\\\h =1\dfrac{1}{2}=\dfrac{3}{2} \ inches$

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

                                                                 $\sf =\dfrac{5}{2}*4*\dfrac{3}{2}\\\\= 5*1*3\\\\= 15 \ in^3$

Cube:

       $\sf side = \dfrac{1}{2} \ inches$

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

                                                $\sf =\dfrac{1}{2}*\dfrac{1}{2}*\dfrac{1}{2}\\\\ =\dfrac{1}{8} \ in^3$

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

                              $\sf = 15 \div \ \dfrac{1}{8}\\\\=15 *\dfrac{8}{1}\\\\= 120$

120 cubes will fit