Geometry

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caseyk

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May 3, 2011
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Problem: There is a kids pool in the shape of a cylinder with a diameter of 4 ft. and a height of 6 in. How many gallons of water can the cylinder hold?

Know:

I know to find the volume of the cylinder; you convert 4 ft. to in. which = 48 in.
Then you take formula for volume of a cylinder: V = Bh or area of the base times the height.
You get: V = (pie)(24)(squared)(6)
V = (pie)(576)(6)
V = 3456(pie) in. cubed "or" V = 288(pie) ft. cubed

I know: 1 cubic ft. = 7.48 gallons

The answer to the problem is 41 gallons, but after i figure out the volume of the cylinder i get lost. How do i get how many gallons it can hold?
 
caseyk said:
Problem: There is a kids pool in the shape of a cylinder with a diameter of 4 ft. and a height of 6 in. How many gallons of water can the cylinder hold?

Know:

I know to find the volume of the cylinder; you convert 4 ft. to in. which = 48 in.
Then you take formula for volume of a cylinder: V = Bh or area of the base times the height.
You get: V = (pie)(24)(squared)(6)
V = (pie)(576)(6)
V = 3456(pie) in. cubed "or" V = 288(pie) ft. cubed

I know: 1 cubic ft. = 7.48 gallons

The answer to the problem is 41 gallons, but after i figure out the volume of the cylinder i get lost. How do i get how many gallons it can hold?
Click to expand...

Since you've calculated the volume in cubic inches, you will have to convert cubic inches to cubic feet (so that you can use the fact that 1 cubic ft. = 7.48 gallons). 1 cubic foot is the volume of a cube which is 1 foot long, 1 foot wide, and 1 foot high. Or....12 inches long, 12 inches wide, and 12 inches high. The volume of such a cube would be 12 inches * 12 inches * 12 inches, or 1728 cubic inches. 1 cubic foot = 1728 cubic inches.

Now you should be able to find out how many cubic feet you've got, and thus how many gallons the pool will hold.

An alternate (and maybe simpler approach) would be to find the volume of the pool in cubic feet right away. The diameter of the pool is GIVEN in feet. The height of the pool is 6 inches....can you express 6 inches in feet? If your radius is in feet, and your height is in feet, you'll get a volume in cubic feet.
 
2 questions

How did you turn cubic inches into cubic feet?

Are you sure that the book tells you that there are 7.48 gallons per cubic foot and that the answer is 41?
 
I took 4 ft. and since there is 12 in. in a ft. i multiplied 12 by 4 getting 48 in. Yes the book says 1 cubic ft. = 7.48 gallons.
 
Do you really hate fractions that much? 6" = ½'

\(\displaystyle Volume = \pi (4/2)^{2}\cdot\frac{1}{2}\;ft^{3}\)
 
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