Question

Devin has a huge aquarium for his fish. The volume of the aquarium is 90 cubic feet. If the height is 3 feet, which of these could NOT be the dimensions or the base?

Answer 1

You know that the aquarium has a volume of V=90ft³ and a height of h=3ft.

To determine which set of dimensions cannot correspond to the dimensions of the base, you have to calculate the volume of the aquarium using each set until you find the set of dimensions that don't give 90ft³ as a result.

To determine the volume of a rectangular prism you have to multiply its width, length, and height following the formula:

`V=\text{wlh}`

Always use h=3ft

Set A

Possible dimensions: 2ft x 15ft x 3ft

`\begin{gathered} V_A=2\cdot15\cdot3 \\ V_A=30\cdot3 \\ V_A=90ft^3 \end{gathered}`

Set B

Possible dimensions: 10ft x 3ft x 3ft

`\begin{gathered} V_B=10\cdot3\cdot3 \\ V_B=30\cdot3 \\ V_B=90ft^3 \end{gathered}`

Set C

Possible dimensions: 8ft x 4ft x 3ft

`\begin{gathered} V_C=8\cdot4\cdot3 \\ V_C=32\cdot3 \\ V_C=96ft^3 \end{gathered}`

Set D

Possible dimensions: 6ft x 5ft x 3ft

`\begin{gathered} V_D=6\cdot5\cdot3 \\ V_D=30\cdot3 \\ V_D=90ft^3 \end{gathered}`

The only set of dimensions that do not lead to a volume of 90ft³ is set C