Mahabir Singh Solutions for Chapter: Areas Related to Circles, Exercise 1: MATHEMATICAL REASONING

If the difference between the area of a regular hexagon and the area of a circle circumscribed in it is $26.705 {\mathrm{cm}}^2$. Find the radius of the circle. [Use $\pi =3.143, \sqrt{3}=1.732$]

The area of two concentric circles are $962.5 {\mathrm{cm}}^2$ and $1386 {\mathrm{cm}}^2$ respectively. The width of the ring is _______ .

A chord of a circle subtends an angle of $60°$ at the centre. If the length of the chord is $100 \mathrm{cm}$. find the area of the major segment.

Find the area of a ring whose outer and inner radii are respectively $23 \mathrm{cm}$ and $12 \mathrm{cm}$

The perimeter of a sector of a circle of radius $5.2 \mathrm{cm}$ is $16.4 \mathrm{cm}$. The area of a sector is ___ .

Circle $C_1$ passes through the centre of the circle $C_2$ and is tangential to it. If the area of $C_1$ is $4 {\mathrm{cm}}^2$ then the area of $C_2$ is _ .

In the given figure $AP=3 \mathrm{cm}$, the area of the shaded region is _____.

The ratio of the outer and inner perimeters of a circular path is $23:22$. If the path is $5$ metres wide, the diameter of the inner circle is ________ .