easy question...

[sinkokuyou]

27.
What is the roaming area of a goat on a 20 ft leash tied to the corner of a shed that is 8 ft by 12 ft?
37.
A thin-walled circular cylinder is filled 85% with water, closed up and then tipped over on a table so it would roll if pushed. What is the height of the water level over the tabletop divided by the cylinder diameter?

[calcguy]

These are geometry problems. Start by drawing diagrams.

06A-27. Draw a 12 × 8 rectangle. From one corner you can draw ¾ of a circle. When the leash hits the 12 ft side, there is 8 ft of leash left over to make an 8 ft quarter circle. When the leash hits the 8 ft side, there is 12 ft left to make a 12 ft quarter circle. Now add the three areas:
¾π(20)² + ¼π(12)² + ¼π(8)² = 1110 ft²

06A-37. This problem was on the 08-09 Study List. Draw a circle with radius 1 that represents the cross section of the cylinder. Draw a chord towards the top to be the water level. Since the cylinder is 85% full, the area of the segment above the chord is (1 — 0.85)π(1)² = 0.15π
Use your equation solver to solve 0.15π = ½(1)²(Θ — sinΘ) for Θ, the angle of the segment. You get Θ = 1.89 rad.
Now cos(1.89/2) = 0.585, the distance from center to chord.
Finally, Ratio = (1 + 0.585)/2 = 0.793