Math

6. The diagram shows the cross section of a cylindrical pipe with water lying in the bottom.
(Since I can't post picture here)
The diagram: ◒
a) If the maximum depth of the water is 2cm and the radius of the pope is 7cm, find the area shaded.

b)What is the volume of water in a pipe length of 30cm?

An equilateral triangle is inscribed in a circle of radius 18.8cm.
the diagram: ⎊
Find:
a)area of the triangle
b)area of the three segments surrounding the triangle.

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1. The area of a segment subtended by an angle θ is
1/2 r^2 (θ - sinθ)
So, what is θ ?
If you draw the diagram, you can see that cos(θ/2) = 5/7

Now, the volume of water is the area of the segment times the length

(b) The side of an equilateral triangle inscribed in a circle of radius r is
s = r√3
And, yu know the area of an equilateral triangle of side s is
a = √3/4 s^2 = √3/4 (3r^2)
And of course, the 3 segments outside the triangle are just the area of the circle less that of the triangle.
So just plug and chug.

And no, I did not know these handy formulas off the top of my head. But it only took me about a minute with google. Try it some time.

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oobleck
2. find angle center theta = 2 cos^-1 ( 5/7 ) = 2 cos^-1 .7143 = 88.8 degrees
A of segment = (1/2)R^2 (theta - sin theta) = (49/2) (theta in radians - sin theta) = 49/2 ( 1.55-1)
= 13.47 cm^2

times 30 = 404 cm^3

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Damon

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