SOLUTION: I have to solve a volume problem and the picture is a slice of pie. The height is 10 in, the side is 5 in and the curve is 16 in. How do I calculate the volume?
I have a pictu
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Question 1200707: I have to solve a volume problem and the picture is a slice of pie. The height is 10 in, the side is 5 in and the curve is 16 in. How do I calculate the volume?
I have a picture of the figure; but, can't upload it. Please help.
I have tried to solve using the cylinder volume formula and then dividing the answer by 4 (only because it looks like a forth-of-a pie).
V=3.14 x 5 x 5 x 10
= 785 in3
then divided by 4 . . . 196.25 in3
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the base of the pie would be the sector of a circle, i believe.
the base forms a circle with a radius of 5 inches.
the area of the base would be equal to pi * r^2 = pi * 5^2 = 25 * pi.
the circumference of the base would be equal to 2 * pi * r = 2 * pi * 5 = 10 * pi
since the curved part of the slice would be 16 inches, then the area of the slice would be pi * 5^2 * 16 / (10 * pi) = 40 square inches.
since the height of the slice is 10 inches, then the volume of the slice will be 10 * 40 = 400 cubic inches.
your way would have worked except for the fact that the slice is not 1/4 of the pie, but 16 / (10 * pi) = .5092958179 of the pie.
take also into account that the volume of the cylinder is 10 * pi * 25 = 785.3981634 and that pi is equal to 3.141592654, and you will get .5092958179 * 785.3981634 = 400 cubic inches, same as i got.
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
Hello,
your pie is a right cylinder, and your piece of the pie is called in Geometry " a sector of a right cylinder ".
See the images at this link
https://www.google.com/search?q=sector+of+a+cylinder+image&rlz=1C1CHBF_enUS910US910&oq=sector+of+a+cylinder+image&aqs=chrome..69i57j33i160.12078j0j15&sourceid=chrome&ie=UTF-8
For such geometry object, the terms " side " is INAPPLICABLE. The relevant term is the " radius ".
The term " curve " is not applicable, too. The relevant term is " the arc of the circle at the base ".
If you want to tell about the length of this " curve ", you should say " the length of the arc at the base ".
Learn the terminology and use it properly - otherwise, the people around will not understand you.
On cylindrical solids, you may read and learn from these lessons
- Volume of cylinders
- Solved problems on volume of cylinders
in this site (at no charge and without registration).
You will find there the links to lessons on other Geometric solids, too.
Come, read and learn.
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