Question 461827: Guess what percentage of the world's population could be packed into a cubical box measuring 1/2 mile on each side. Assume that the world's population is 6.6 billion and that the volume of a typical person is about 2 cubic feet.
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Guess what percentage of the world's population could be packed into a cubical box measuring 1/2 mile on each side. Assume that the world's population is 6.6 billion and that the volume of a typical person is about 2 cubic feet.
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This problem has several steps: (1) We need to find the volume of the cubical box. We must express the volume in cubic feet rather than cubic miles, since we have the "average human volume" in cubic feet. Then, (2) we need to compare the box volume with the volume of the average person, and (3) express that comparison as a percentage.
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Note: Usually, the word "guess" means "estimate" in math. However, I'll go ahead and work out the arithmetic, and leave the estimating to you.
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Compute the volume of the box (in cubic feet).
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The formula for the volume of a cube is [side length]^3. We are given the side length of 1/2 mile. Let's convert that to feet. There are 5,280 feet in a mile. I want to know how many feet there are in a 1/2 mile, so I multiply (5280 * 1/2 = 2640). There are 2,640 feet in a 1/2 mile.
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Now we can use the volume formula to calculate the number of cubic feet:
Volume = (2640)^3 = 18,399,744,000. There are 18,399,744,00 cubic feet in our box.
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Calculate how many average humans will fit in the box.
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One average human takes up 2 cubic feet. We want to know how many average humans will fit in 18,399,744,000 cubic feet, so we divide (18,399,744,000 / 2 = 9,199872000). So approximately 9,199,872,000 people fit in the box.
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Compare the two populations and convert to a percentage.
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We see that the population inside the box is larger than the total population of the world! The ration that compares the population in the box to the total population is:
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We convert the decimal 1.394 to a percentage by multiplying by 100.
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About 139.4% o the world's population would fit in a cubical box measuring 1/2 mile on each side.
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If you'd like to see this problem solved using scientific notation, look at question #427998 using the search box on the front page of www.algebra.com.
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Hope this helps!
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Ms. Figge
math-in-the-vortex
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