Question

The diagram shows the cross section of a cylindrical pipe with water lying in the bottom.

Answer 1

Hey 

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. 

What you do now is the following: 

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7) 

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8° 

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram. 

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8° 
= 88.8/360*π*7² - 24.5*sin 88.8° 
≃ 13.5 cm² 
(using area of ∆ = ½.a.b.sin C for the triangle) 



b) 

volume of water = cross-sectional area * length 
≃ 13.5 * 30 cm³ 
≃ 404 cm³

Hoped it Helped