(D) The lighthouse spreads light over a sector of a circle with radius $r = 16.5 \, km$ and central angle $\theta = 80^{\circ}$.The area of the sector

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(D) The lighthouse spreads light over a sector of a circle with radius $r = 16.5 \, km$ and central angle $\theta = 80^{\circ}$.The area of the sector is given by the formula:$\text{Area} = \frac{\theta}{360^{\circ}} \times \pi r^2$Substituting the given values:$\text{Area} = \frac{80^{\circ}}{360^{\circ}} \times 3.14 \times (16.5)^2$$= \frac{2}{9} \times 3.14 \times 272.25$$= \frac{2}{9} \times 854.865$$= 189.97 \, km^2$Thus,the area of the sea over which the ships are warned is $189.97 \, km^2$.

Class 10 Mathematics Areas Related to Circles Areas of Sector and Segment of a Circle

Difficult

To warn ships for underwater rocks,a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of $16.5 \, km$. Find the area of the sea over which the ships are warned. (in $km^2$) (Use $\pi=3.14$)

A
$185.14$
B
$205$
C
$36.84$
D
$189.97$

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Areas Related to Circles

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Areas of Sector and Segment of a Circle

In the figure,$ABC$ is a quadrant of a circle of radius $14 \, cm$ and a semicircle is drawn with $BC$ as diameter. Find the area of the shaded region. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

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Find the area of the shaded region in the figure,where a circular arc of radius $6 \, cm$ has been drawn with vertex $O$ of an equilateral triangle $OAB$ of side $12 \, cm$ as centre. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

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In a circle with radius $11.2 \, cm$,two radii are perpendicular to each other. Find the area of the minor sector,the major sector,and the minor segment corresponding to these radii.

Medium

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$A$ car has two wipers which do not overlap. Each wiper has a blade of length $25 \, cm$ sweeping through an angle of $115^{\circ}.$ Find the total area cleaned at each sweep of the blades. [use $\pi=\frac{22}{7}$]

Medium

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The length of the minute hand of a clock is $7\,cm$. The area of the region swept by it in $20$ minutes is $\ldots \ldots \ldots \,cm^2$.

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To warn ships for underwater rocks,a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of $16.5 \, km$. Find the area of the sea over which the ships are warned. (in $km^2$) (Use $\pi=3.14$)

Similar Questions

In the figure,$ABC$ is a quadrant of a circle of radius $14 \, cm$ and a semicircle is drawn with $BC$ as diameter. Find the area of the shaded region. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

Find the area of the shaded region in the figure,where a circular arc of radius $6 \, cm$ has been drawn with vertex $O$ of an equilateral triangle $OAB$ of side $12 \, cm$ as centre. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

In a circle with radius $11.2 \, cm$,two radii are perpendicular to each other. Find the area of the minor sector,the major sector,and the minor segment corresponding to these radii.

$A$ car has two wipers which do not overlap. Each wiper has a blade of length $25 \, cm$ sweeping through an angle of $115^{\circ}.$ Find the total area cleaned at each sweep of the blades. [use $\pi=\frac{22}{7}$]

The length of the minute hand of a clock is $7\,cm$. The area of the region swept by it in $20$ minutes is $\ldots \ldots \ldots \,cm^2$.

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