Question

Miss Wilton is planning a rectangular flower box for her front window she wants the flower box to hold exactly 16 cubic feet of soil how many boxes with different size bases will hold exactly 16 cubic feet of soil using whole number dimensions

Answer 1

Answer:

Three rectangular boxes having bases 4 cubic feet, 3 cubic feet and 2 cubic feet respectively will be required to hold 16 cubic feet of soil.

The dimensions of the three rectangular boxes will be 4 \times 1 \times 2, 3 \times 1 \times 2, and 2 \times 1 \times 1.

Step-by-step explanation:

The total soil to be held is 16 cubic feet.

The volume of a rectangular box is given by the product, lbh, where l is the length, b is the base and h is the height.

16 cubic feet of volume can be divided into two different volumes having values 8 cubic feet, 6 cubic feet and 2 cubic feet, to get two set of dimensions having different bases.

To get the first value of volume, 8 cubic feet, the length, base and height can be 1 foot, 4 feet and 2 feet respectively.

To get the second value of volume, 6 cubic feet, the length, base and height can be 1 foot, 3 feet and 2 feet respectively.

To get the other value of volume, 2 cubic feet, the length, base and height can be 1 foot, 2 feet and 1 foot respectively.

Since, all the three boxes have to be rectangular in shape, the base has to be more than the other two dimensions to get the required volumes as explained above.

If the number of rectangular boxes are increased, the dimensions would not be whole numbers as per the requirement.

The above mentioned can be shown in calculations as given below.

Volume of the first rectangular box

= lbh

= 1 \times 4 \times 2

= 8

Thus, the volume of the first rectangular box is 8 cubic feet.

Volume of the second rectangular box

= lbh

= 1 \times 3 \times 2

= 6

Thus, the volume of the second rectangular box is 6 cubic feet.

Volume of the other rectangular box

= lbh

= 1 \times 2 \times 1

= 2

Thus, the volume of the third rectangular box is 2 cubic feet.

Total volume of both boxes

= 8 + 6 + 2

= 16 cubic feet