R. D. Sharma Solutions for Chapter: Areas Related to Circles, Exercise 4: EXERCISE 13.4

In Fig., an equilateral triangle $ABC$ of side$6 \mathrm{cm}$ has been inscribed in a circle. Find the area of the shaded region. $($Take $\mathrm{\pi }=3.14)$

$ABCDEF$ is a regular hexagon with centre $\mathrm{O}$ as shown in the figure. If the area of the triangle $OAB$ is $9{\mathrm{cm}}^2$, find the area of the circle in which the hexagon is inscribed.

In the following figure, the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is $14 \mathrm{cm}$ and of the smallest is $3.5 \mathrm{cm}$, find the area of the shaded region. If the required answer is $x {\mathrm{cm}}^2$, what is the value of $x$?

The figure below shows the cross-section of the railway tunnel. The radius $\mathrm{OA}$ of the circular part is $2 \mathrm{m}$. If $\angle \mathrm{AOB}=90°$, If  the perimeter of the cross-section is $A m$, then find the value of $A$ rounded off to two decimal places. Take $\sqrt{2}=1.414, \mathrm{\pi }=3.14$.

The figure below shows the cross-section of railway tunnel. The radius $\mathrm{OA}$ of the circular part is $2 \mathrm{m}$. If $\angle \mathrm{AOB}=90°$ and the area of the cross-section, rounded off to two decimal places is $k {\mathrm{m}}^2$, then find the value of $k$. (Take $\mathrm{\pi }=\frac{22}{7}$) 

Sides of a triangular field are $15 \mathrm{m}, 16 \mathrm{m}$ and $17 \mathrm{m}$. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length $7$ $\mathrm{m}$ each to graze in the field. Find the area of the field which cannot be grazed by three animals.

In the figure, the side of square is $28 \mathrm{cm}$, and radius of each circle is half of the length of the side of the square where $\mathrm{O}$ and $\mathrm{O}\text{'}$ are centres of the circles. Find the area of shaded region.

In a hospital used water is collected in a cylindrical tank of diameter $2 \mathrm{m}$ and height $5 \mathrm{m}$. After recycling, this water is used to irrigate a park of hospital whose length is $25 \mathrm{m}$ and breadth is $20 \mathrm{m}$. If tank is filled completely then what will be the height of standing water used for irrigating the park?