A mermaid has a terrarium that measures 42 inches × 10 inches × 9 inches. She also has a box that measures 3 inches × 3 inches × 3 inches. Every minute, the mermaid fills the box with sand from her backyard and then pours the sand into the terrarium. How many minutes does it take the mermaid to fill three-quarters of the terrarium with sand?

9514 1404 393

  105 minutes

Step-by-step explanation:

The volume of the terrarium is ...

  V = LWH

  V = (42 in)(10 in)(9 in) = 3780 in³

The volume of a box is ...

  V = (3 in)(3 in)(3 in) = 27 in³

Then the number of boxes it takes to fill the terrarium is ...

  (3780 in³)/(27 in³/box) = 140 boxes

The mermaid wants to fill it 3/4 full, so only needs 3/4 this number of boxes. That is 105 boxes. At the rate of 1 per minute, ...

  it will take 105 minutes to fill 3/4 of the terrarium

i believe the answer is the polygon, heptagon.