Question

Elena needs to find a table that will fit three cube-shaped cases, each containing a frog.

If the volume of each case is 1,000 cubic inches, could she use a table with a top that measures 2 1/2 feet long and 1 1/2 feet wide?

Explain.

Answer 1

The area of the table is 3.75 feet
The boxes are .83333 feet by .83333 feet so that area is .69
.69x3 is 2.07 so yes they will fit on top of the table

Answer 2

Elena can make use of the table, since the area of the table measures 540 in² and it is greater than the combined area of the cubes which is 300 in²

The volume of a cube can be obtained using the formula:

• Volume, V = a³ ; Where, a = edge of cube

The given volume of the cube, V = 1000 in³

V = a ³

1000 = a³

Take the cube root of both sides ;

a = 10 inches

The Area of the cube is thus ;

Area = a²

Area of cube = 10² = 100 in²

The Area of the three cubes :

• 100 in² × 3 = 300 in²

The area of the table :

Converting the dimension to inches :

1 foot = 12 inches

Length = 2.5 feets = (12 × 2.5) = 30 inches

Width = 1.5 feets = (12 × 1.5) = 18 inches

Hence,

Area of table in feet = length × width = 30 × 18 = 540 in²

Therefore, Since the area of the table is greater than the combined areas of the cubes, then, the table is usable.

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