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a_sh-v
14 days ago
10

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

Mathematics
1 answer:
PIT_PIT [9.1K]14 days ago
5 0
Hello

So my brother shared this on Yahoo
To start, draw a line connecting the circle's center to one endpoint of the chord (water surface) and again to the point with maximum depth. This creates a right triangle. The length of the side up to the water-surface measures 5 cm, and the hypotenuse is 7 cm.

<span>Now, perform the following steps: </span>

<span>Calculate angle θ at the right triangle's corner using: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7) </span>

<span>Thus, θ is approximately 44.4°, leading to the angle subtended at the circle center by the water surface being roughly 88.8°. </span>

<span>To find the shaded area, subtract the triangular area above the water in your diagram from the area of the sector. </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>which is approximately 13.5 cm² </span>
<span>(using area of ∆ = ½.a.b.sin C for the triangle) </span>



<span>b) </span>

<span>The water's volume is equal to the cross-sectional area multiplied by the length </span>
<span>≈ 13.5 * 30 cm³ </span>
<span>≈ 404 cm³</span>

I hope this was helpful
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Got it!
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