R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 16A

A sector is cut from a circle of radius $21 \mathrm{cm}$. The angle of the sector is $150°$. Find the length of the arc and the area of the sector. [Take $\mathrm{\pi }=\frac{22}{7}$]

A chord $PQ$ of the circle of radius $10 \mathrm{cm}$ subtends an angle of $60°$ at the centre of the circle. If the sum of areas of minor and major segment is $k {\mathrm{cm}}^2$, find the value of $k$. [Take $\mathrm{\pi }=3.14$]

A chord $10 \mathrm{cm}$ long is drawn in a circle whose radius is $5\sqrt{2} \mathrm{cm}$. Find the areas of both the segments. [take $\pi =3.14$]

Also find the sum of area of both the segments in ${\mathrm{cm}}^2$.

The wheel of a motorcycle is of radius $35 \mathrm{cm}$. How many revolutions per minute must the wheel make so as to keep a speed of $66 \mathrm{km}/\mathrm{hr}?$

Three semicircles each of diameter $3 \mathrm{cm}$, a circle of diameter $4.5 \mathrm{cm}$ and a semicircle of radius $4.5 \mathrm{cm}$are drawn in the given figure. Find the area of the shaded region.

In the given 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 $O$ and $O\text{'}$ are centres of the circles. Find the area of shaded region.   

With the vertices $A, B$ and $C$ of a triangle $ABC$ as centres, arcs are drawn with radii $5 \mathrm{cm}$ each as shown in the given figure. If $AB=14 \mathrm{cm}, BC=48 \mathrm{cm}$ and $CA=50 \mathrm{cm}$ then find the area of the shaded region. [Use$\mathrm{\pi }=3.14$]

If the diameters of the concentric circles shown in the figure below are in the ratio $1:2:3$ then find the ratio of the areas of three regions.