Question

A flower box in the shape of a right rectangular prism is made of thin metal, shown below. The box has length 90 centimeters (cm), width 45 cm, and height 45 cm. The box is 85 percent filled with soil. Each bag of soil holds 1 cubic (ft^3), and 1 ft^3 is approximately 28,316 cubic centimeters (cm^3). How many bags of soil are needed to finish filling the flower box?

A. 1 bag

B. 2 bags

C. 6 bags

D. 7 bags

Answer 1

A. 1 bag

Explanation:

A flower box is in the shape of a right rectangular prism which has dimensions:

Length = 90 cm

Width = 45 cm

Height = 45 cm

The box is 85% filled with soil, so the volume of the soil is;

Volume of a triangular prism = Length × Width × Height

`(85)/(100)` × 90 cm × 45 cm × 45 cm = 154912.5 cm³

Each bag of soil holds 1 ft³ ≅ 28316 cm³

The volume of soil needed to finish filling the flower box is 100% - 85% = 0.15 of the box's volume = 0.15 × 90 cm × 45 cm × 45 cm = 27337.5 cm³

1 bag of soil ≅ 28316cm³

How many bags of soil ≅ 27337.5 cm³

Cross multiplying gives;

`(27337.5 cm^3)/(28316cm^3)` × 1 bag ≅ 0.9654435655 bags

Since we cannot have 0.9 bags, we need 1 full bag so that the remaining space in the flower box can be filled with soil.