Embibe Experts Solutions for Chapter: Areas Related to Circles, Exercise 1: Nagaland Board-2019

In a circle of radius $28 \mathrm{cm}$, an arc subtends an angle $90°$ at the centre. Find the perimeter of the sector.

A rectangle of dimensions $16\mathrm{cm}\times 12\mathrm{cm}$ is inscribed in a circle. Find the area enclosed between the circle and the rectangle.

In the adjoining figure, $ABCD$ is a square of side $20 \mathrm{cm}$. Four circles of equal radii $7 \mathrm{cm}$ are drawn on its four vertices. Find the area of the shaded region. (Use $\mathrm{\pi }=3.14$)

The length of a minute hand of a clock is $14 \mathrm{cm}$. Find the area swept by the minute hand in $10 \mathrm{minutes}$. [Use $\pi =\frac{22}{7}$]

A wire bent in the form of a square encloses an area of $1936 {\mathrm{cm}}^2$. If the same wire is bent into a circle, find the area enclosed by it.

A sector of arc length $22 \mathrm{cm}$ and central angle $60°$ is cut off from a circular metal disc. Find the perimeter of the remaining portion of the disc.

The wheels of a car are of diameter $80 \mathrm{c}\mathrm{m}$ each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of $66 \mathrm{k}\mathrm{m}$ per hour? $\left(\mathrm{use} \pi =\frac{22}{7}\right)$

The area of an equilateral triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ is $17320.5 \mathrm{c}{\mathrm{m}}^2.$ With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle as shown in the figure. Find the area of shaded region. (Use $\mathrm{\pi }=3.14$ and $\sqrt{3}=1.73205$)