Question

To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)

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Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar \: {\pmb{\sf{\underline{Understanding \: the \: Question...}}}}}$

⋆ This question says that we have to find out the area of the sea over which the ships are warned. Given that: To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80 degrees, means there is light over a sector of angle to a distance of 16.5 kilometres. As it's a sector henceforth, the distance be the radius of the circle. It is also given that we have to take the value of π as 3.14 It is also cleared that we have to use formula regard where π is used. Let us see how to solve this question properly!

${\bigstar \: {\pmb{\sf{\underline{Given \: that...}}}}}$

⠀⠀⠀⠀ ⠀⠀⠀To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km.

⋆ Radius = 16.5 kilometres

⋆ Angle = 80 degrees

${\bigstar \: {\pmb{\sf{\underline{To \: find...}}}}}$

⋆ The area of the sea over which the ships are warned.

${\bigstar \: {\pmb{\sf{\underline{Solution...}}}}}$

⋆ The area of the sea over which the ships are warned = 189.97 km²

${\bigstar \: {\pmb{\sf{\underline{Using \: concept...}}}}}$

⋆ Formula to find out the area of the sector of a circle.

${\bigstar \: {\pmb{\sf{\underline{Using \: formula...}}}}}$

• Remember that the formula to find out the area of circle is πr²? Nice!

${\underline{\boxed{\pmb{\sf{\star \: \dfrac{\theta}{360 \degree} \times \pi r^2}}}}}$

${\bigstar \: {\pmb{\sf{\underline{Where...}}}}}$

⋆ θ denotes angle

⋆ θ is pronounced as theta

⋆ π is pronounced as pi

⋆ The value of π is 22/7 or 3.14

⠀⠀⠀⠀ ⠀⠀(But according to the question, we have to take the value of π as 3.14)

⋆ r denotes radius

${\bigstar \: {\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ Now we just have to use the given formula and have to put the values according to that and at last we get our final result very easily! Let's do it!

$:\implies \sf \dfrac{\theta}{360 \degree} \times \pi r^2 \\ \\ :\implies \sf \dfrac{80}{360} \times 3.14 \times (16.5)^{2} \\ \\ :\implies \sf \dfrac{8{\cancel{0}}}{36{\cancel{0}}} \times 3.14 \times (16.5)^{2} \\ \\ :\implies \sf \dfrac{8}{36} \times 3.14 \times (16.5)^{2} \\ \\ :\implies \sf \cancel{\dfrac{8}{36}} \times 3.14 \times (16.5)^{2} \\ \\ :\implies \sf \cancel{\dfrac{4}{18}} \times 3.14 \times (16.5)^{2} \\ \\ :\implies \sf \dfrac{2}{9} \times 3.14 \times (16.5)^{2} \\ \\ :\implies \sf \dfrac{2}{9} \times 3.14 \times 16.5 \times 16.5 \\ \\ :\implies \sf \dfrac{2}{9} \times 3.14 \times 272.25 \\ \\ :\implies \sf \dfrac{2}{9} \times 8548.50 \\ \\ :\implies \sf 189.97 \: km \: sq. \\ \\ {\pmb{\sf{Hence, \: 189.97 \: km \: sq. \: is \: area \dots \dots}}}$

${\large{\pmb{\sf{\underline{AdditioNal \: Knowledge...}}}}}$

★ The region between the chord and either of it's arcs is known as the segment of a circle or a circular region.

★ There are two type of segments that are major segment and minor segment.

★ The region between an arc and the two radii, joining the centre to the end points of the arc is known as sector.

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• Kindly see the diagram regard question from attachment 2nd.

Answer 2

this photo is your answer