The diagram shows the cross section of a cylindrical pipe with water lying in the bottom.
a.. if the maximum depth of water is 2cm and radius of the pipe is 7cm, find the area shaded.
what is the volume of water in a length of 30cm

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

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