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A flower box in the shape of a right rectangular prism is made of thin metal, shown above. The box has length 909090 centimeters (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis, width 45\,\text{cm}45cm45, start text, c, m, end text, and height 45\,\text{cm}45cm45, start text, c, m, end text. The box is 858585 percent filled with soil. Each bag of soil holds 111 cubic foot (\text{ft}^3)(ft 3 )left parenthesis, start text, f, t, end text, cubed, right parenthesis, and 1\,\text{ft}^31ft 3 1, start text, f, t, end text, cubed is approximately 28{,}31628,31628, comma, 316 cubic centimeters (\text{cm}^3)(cm 3 )left parenthesis, start text, c, m, end text, cubed, right parenthesis. How many bags of soil are needed to finish filling the flower box? Choose 1 answer: 1

Respuesta :

Answer:

Approximately 5 bags would be needed.

Step-by-step explanation:

Given,

The rectangular flower box has,

Length = 90 cm

Width = 45 cm

Height = 45 cm

So, its volume = length × width × height

                        = 90 × 45 × 45

                        = 182250 cm³,

Now, it is 85 percent filled with soil.

Thus, the quantity of soil in the box = 85% of its volume

                                                           = 85% of 182250

                                                           = 0.85 × 182250

                                                           = 154912.5 cm³

Again, each bag of soil holds 1 cubic foot of soil.

1 ft³ = 28316.8 cm³

Thus, cube cm hold by each bag = 28316.8 cm³

Hence,

The required numbers of bags = [tex]\frac{\text{total soil}}{\text{Soil in each bag}}[/tex]

                                                    [tex]=\frac{154912.5}{28316.8}[/tex]

                                                    ≈ 5