Question 720101: Please I need help. I did it for homwork but i got it wrong the problem says
A rectangular box measures 18 inches wide, 15 inches long, and 10 inches high.
A.) What is the volume of the box in cubic inches? In cubic feet?
B.) A big bag of packing peanuts says that it holds 1.2 cubic feet of peanuts. How much more peanuts are needed to fill the box, or how much extra is there?
C.) What part(fraction) of a box will the peanuts fill, or how many boxes of this size will the peanuts fill? Express the answer as a fraction, then as a decimal.
D.) How high up in the box will the peanuts come?
E.) Explain how questions b, c, and d are similar and how are they different
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! answers are shown below:
A rectangular box measures 18 inches wide, 15 inches long, and 10 inches high.
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A.) What is the volume of the box in cubic inches? In cubic feet?
since the measurements of the box are already in inches, then the volume is equal to 18 * 15 * 10 which is equal to 2700 cubic inches.
you need to convert inches to feet and then do the calculation again.
since 18 inches / 12 = 1.5 feet and 15 inches / 12 = 1.25 feet and 10 inches / 12 = .833333333 feet, your volume is equal to 1.5 * 1.25 * .833333333 which is equal to 1.5625 cubic feet.
alternatively, you could have taken the number of cubic inches and divided them by the number of cubic inches per cubic foot.
the number of cubic inches per cubic foot is equal to 12 * 12 * 12 which is equal to 1728 cubic inches per cubic foot.
your original answer in cubic inches was 2700 cubic inches.
divide 2700 cubic inches by 1728 cubic inches per cubic foot and you get 1.5625 cubic feet.
you get the same answer derived in a different, but equivalent, way.
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B.) A big bag of packing peanuts says that it holds 1.2 cubic feet of peanuts. How much more peanuts are needed to fill the box, or how much extra is there?
since the volume of the box is 1.5625 cubic feet and the volume of the peanuts is equal to 1.2 cubic feet, then the difference in cubic feet of peanuts is required to fill the box.
1.5625 - 1.2 cubic feet equals .3625 cubic feet.
this means you need another .3625 cubic feet of peanuts to fill the box.
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C.) What part(fraction) of a box will the peanuts fill, or how many boxes of this size will the peanuts fill? Express the answer as a fraction, then as a decimal.
the peanuts will fill 1.2 / 1.5625 = .768 of the volume of the box.
the decimal is .768
the fraction is 1.2 / 1.5625 which i was able to simplify to 96 / 125.
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D.) How high up in the box will the peanuts come?
to find this, you need to freeze the length and the width of the box and then solve for the height using the volume of the peanuts.
the length of the box is 1.2 feet and width of the box is 1.5 feet.
the volume of the peanuts is 1.2 cubic feet.
length * width * height = volume
this translates to:
1.25 * 1.5 * height = 1.2 cubic feet.
simplify this equation to get:
1.875 square feet * height = 1.2 cubic feet
divide both sides of this equation by 1.875 to get:
height = 1.2 cubic feet divided by 1.875 square feet = .64 feet.
the height of the peanuts in the box is equal to .64 feet.
to confirm, calculate the volume of the peanuts in the box.
the volume of the peanuts in the box is equal to 1.25 * 1.5 * .64 which is equal to 1.2 cubic feet.
you needed to freeze the length and the width and allow the height to vary.
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E.) Explain how questions b, c, and d are similar and how are they different.
questions b, c, and d all involve the volume of the peanuts in relationship to the volume of the box.
b asks for the volume of the peanuts in the box.
c asks for the ratio of the volume of the peanuts in the box to the volume of the box.
d asks for the height of the peanuts in the box which is a function of the formula for the volume of the peanuts in the box.
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