Question

milton got a paperweight like the one shown below. he needs to fill it with sand to give it weight. note figure is not drawn to scale. if a = 3 inches, what is the volume of the paperweight? a. 81 cubic inches b. 126 cubic inches c. 108 cubic inches d. 54 cubic inches

Explanation:

Step1: Find volume of large rectangular - prism

The volume formula for a rectangular - prism is $V = l\times w\times h$. For the large rectangular - prism with length $a$, width $a$, and height $2a$, its volume $V_1=a\times a\times2a = 2a^{3}$.

Step2: Find volume of small rectangular - prism

For the small rectangular - prism with length $a$, width $a$, and height $a$, its volume $V_2=a\times a\times a=a^{3}$.

Step3: Find total volume of paperweight

The total volume $V$ of the paperweight is $V = V_1+V_2=2a^{3}+a^{3}=3a^{3}$.

Step4: Substitute $a = 3$ inches

Substitute $a = 3$ into the formula $V = 3a^{3}$. Then $V=3\times3^{3}=3\times27 = 81$ cubic inches.

Answer:

A. 81 cubic inches