So my brother posted this on Yahoo Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.
<span>What you do now is the following: </span>
<span>Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7) </span>
<span>So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8° </span>
<span>The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram. </span>
<span>Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8° </span> <span>= 88.8/360*π*7² - 24.5*sin 88.8° </span> <span>≃ 13.5 cm² </span> <span>(using area of ∆ = ½.a.b.sin C for the triangle) </span>
<span>b) </span>
<span>volume of water = cross-sectional area * length </span> <span>≃ 13.5 * 30 cm³ </span> <span>≃ 404 cm³</span>
the y axic corresponds to the price in dollars so in the ordered paid at point a, the y value 30 means that the price of carpet is $30 for the x value of 20 square feet of carpet