Question

The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use the value = 3.14

Answer 1

Solution :-

we know that,

• π radian = 180° .
• Area of sector = (θ/360°) * π * (radius)² {where θ is angle at centre in degree.}
• Area of ∆ = (1/2) * Base * Perpendicular height .

given that,

• Angle at centre = 2.21 radians .
• Radius = r = 30 feet .
• Base of ∆ = 20 feet.
• Perpendicular height of ∆ = 25 feet .

so,

→ π radian = 180°

→ 1 radian = (180/π)°

→ 2.21 radian = {(180/π) * 2.21}°

then,

→ θ = {(180/π) * 2.21}°

→ (θ/360°) = {(180/π) * 2.21}° * 1/360°

→ (θ/360°) = (2.21/2π)°

so,

→ Area of pool = 2(Area of sector) + 2(Area of ∆)

→ Area of pool = 2(Area of sector + Area of ∆)

→ Area of pool = 2[(2.21/2π) * π * (30)² + (1/2) * 20 * 25]

→ Area of pool = 2[2.21 * 450 + 250]

→ Area of pool = 2(994.5 + 250)

→ Area of pool = 2 * 1244.5

→ Area of pool = 2489 ≈ 2490 feet². (Ans.)

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