(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 Textbook - Areas Related to Circles

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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Textbook - Areas Related to Circles

The length of the minute hand of a clock is $14 \, cm$. Find the area swept by the minute hand in $5 \, minutes$. [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 the given figure,$OACB$ is a quadrant of a circle with centre $O$ and radius $3.5 \, cm$. If $OD = 2 \, cm$,find the area of the:
$(i)$ quadrant $OACB$,
$(ii)$ shaded region. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

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In a circular table cover of radius $32 \, cm$,a design is formed by leaving an equilateral triangle $ABC$ in the middle as shown in the figure. Find the area of the design. [Use $\pi = \frac{22}{7}$]

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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

The length of the minute hand of a clock is $14 \, cm$. Find the area swept by the minute hand in $5 \, minutes$. [use $\pi = \frac{22}{7}$]

$AB$ and $CD$ are respectively arcs of two concentric circles of radii $21\, cm$ and $7\, cm$ with centre $O$ (see figure). If $\angle AOB = 30^{\circ}$,find the area of the shaded region.

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 the given figure,$OACB$ is a quadrant of a circle with centre $O$ and radius $3.5 \, cm$. If $OD = 2 \, cm$,find the area of the:$(i)$ quadrant $OACB$,$(ii)$ shaded region. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

In a circular table cover of radius $32 \, cm$,a design is formed by leaving an equilateral triangle $ABC$ in the middle as shown in the figure. Find the area of the design. [Use $\pi = \frac{22}{7}$]

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In the given figure,$OACB$ is a quadrant of a circle with centre $O$ and radius $3.5 \, cm$. If $OD = 2 \, cm$,find the area of the:
$(i)$ quadrant $OACB$,
$(ii)$ shaded region. $\left[ \text{Use } \pi = \frac{22}{7} \right]$