Capacity - Gallons

[Guest]

I came across this problem:

A cylindrical tank is 3 ft. in diameter and 10 ft. in length. Determine capacity in gallons.

My solution:

Volume of cylinder - pi x radius ^2 x height (or length).

3.1416 x 1.5 x 1.5 x 10 = 70.686 cu. ft.

70.686 x 7.48 (cu. ft. to gallons) = 528.73 gal.


Solution provided with problem:

To obtain capacity in gallons, divide volume in cu. in. by 231, or in cu. ft. by 1.337

3^2 x .7854 x 10 = 7.068 x 10 = 70.68 cu. ft.

One gallon = 1.337 cu ft.

70.68 / 1.337 = 52.86 gal.

Which is correct ?

[Guest]

There are 231 cu. inches in a gallon, so divide the volume in cu.ins by 231 to get gallons
and 1 cu. ft = 6.25 gall, so multiply the volume in cu. ft by 6.25 to get gallons

[Guest]

Thanks.

I have a question:

3^2 x .7854 x 10 = 7.068 x 10 = 70.68 cu. ft.

My question - Why is 10 used twice ?

[Guest]

Sorry error in last post..... check out US gallons and imperial gallons....

There are 231 cu. inches in a US gallon, so divide the volume in cu.ins by 231 to get US gallons....US gallons liquid
and 1 cu. ft = 7.28 US gallons liquid, so multiply the volume in cu. ft by 7.28 to get gallons liquid....and.....
This is the same as if volume is in cu. ft .... then divide volume cu.ft by 0.1337

1 / 7.48 = 0.1337 .... so there is a typo error ( 1.337 ) in your original post with the question.

[Guest]

Sorry and there is still a typo error in my last post...

and 1 cu. ft = 7.28 US gallons liquid, so multiply the volume in cu. ft by 7.28 to get gallons liquid....and.....

It should read....

and 1 cu. ft = 7.48 US gallons liquid, so multiply the volume in cu. ft by 7.48 to get gallons liquid....and.....

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[Guest]

Thanks again.

[Guest]

Your query........

I have a question:

3^2 x .7854 x 10 = 7.068 x 10 = 70.68 cu. ft.

My question - Why is 10 used twice ?

They used the formula Pi/4 x d^2 x 10 for the volume

pi / 4 = 0.7854 ... and.....d^2 = 3^2 = 9

so that becomes 9 x 0.7854 x 10 ......which gives 7.068 x 10 .... which gives ....70.68 cu ft.

and divide that by 0.1337 ... gives 70.68 / 0.1337 = 528.65 US gallons liquid

[Guest]

Thanks.