Question

Two right rectangular prisms are shown below. 2 inches 5 Inches 9 inches inches 7 NI inches inches Prism I Prism II If each prism is packed with small cubes of side length 1 inch, how many more cubes are in Prism Il than in Prism I? O 42 cubes О 210 cubes O 510 cubes O 720 cubes

Answer 1

The number of small cubes in the prism I can be determined as,

`\begin{gathered} N_1=\frac{Volume\text{ of prism I}}{Volume\text{ of one small cube}} \\ =\frac{(7)/(4)\text{ in}*(5)/(4)\text{ in}*(3)/(2)\text{ in}}{(1)/(4)\text{ in}*(1)/(4)\text{ in}*(1)/(4)\text{ in}} \\ =210 \end{gathered}`

The number of cubes in the prism II can be determined as,

`\begin{gathered} N_2=\frac{2\text{ in}*(5)/(2)\text{ in}*(9)/(4)in}{(1)/(4)in*(1)/(4)in*(1)/(4)in} \\ N_2=720 \end{gathered}`

The difference in the number of cubes is,

`\begin{gathered} N_2-N_1=720-210 \\ =510 \end{gathered}`

Thus, Prism II has 510 more cubes than Prism I.

Thus, option (c) is the correct solution.