Question

To warn ships for under water rocks, a light-house
throws a red coloured light over a sector of 95°
angle to a distance of 16.5 km. Find the area of
the sea over which the ships are warned. [Take π=3.14] best answerer will be marked the brainliest
$(take \: \pi = 3.14 )$
​

Answer 1

Correct Question:

To warn ships for underwater rocks, a lighthouse spreads a red coloured 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 )

Given:

radius, r = 16.5 Km

angle of sector, $\bold{\theta }$ = 80°

We know,

Area of Sector = $\boxed{\pi r^{2} \frac{\theta }{360}}$

$</p><p>\rightarrow \quad 3.14 \times 16.5 \times 16.5 \times \frac{\cancel{80}}{\cancel{360}}</p><p>\\ \\ </p><p>\rightarrow \quad 31.4 \times 16.5 \times 16.5 \times \frac{1}{45} </p><p>\\ \\ </p><p>\rightarrow \quad 31.4 \times \cancel{272.25} \times \frac{1}{\cancel{45}} \\ \\ \rightarrow \quad 31.4 \times 6.05 \\ \\ \rightarrow \quad \bold{189.97 \; km^{2}}</p><p>$

Answer 2

$\Huge{\underline{\underline{\mathfrak{\red{Question :}}}}}$

To warn ships for underwater rocks, a lighthouse spreads a red coloured 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. ( Take π = 3.14 ).

$\rule{100}{2}$

$\Huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Given :

Angle (θ) is 80°

Radius (r) = 16.5 km

π = 3.14

Now, use formula for area of sector :

$\LARGE \implies {\boxed{\boxed{\red{\sf{\frac{\pi r^2 \theta }{360^{\circ}}}}}}}$

(Putting Values)

$\Large \leadsto {\sf{\frac{3.14 \: \times \: (16.5)^2 \: \times \: \cancel{80}}{\cancel{360}}}}$

$\Large \leadsto {\sf{\frac{3.14 \: \times \: \cancel{272.5}}{\cancel{4.5}}}}$

$\Large \leadsto {\sf{3.14 \: \times \: 60.5}}$

$\Large{\boxed{\red{\sf{Area \: = \: 189.97 \: km^2}}}}$

$\rule{200}{2}$

Additional Information

Formulas :-

• Formula for area of sector is πr²θ/360°
• Formula for length of an arc is πrθ/360°
• Formula for Perimeter of a sector is 2r + (πr²θ/360°)
• Formula for area of major sector is πr² - (πr²θ/360°)