O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 2: Exercise

Find the area enclosed between two concentric circles of radii $3.5 \mathrm{cm}$and $7 \mathrm{cm}$. A third concentric circle is drawn outside the $7 \mathrm{cm}$circle so that the area enclosed between it and the $7 \mathrm{cm}$ circle is the same as that between the two inner circles. Find the radius of the third circle, correct to one decimal place.

A circular field has a perimeter of $650 \mathrm{m}$. A plot, in the shape of a square having its vertices on the circumference of the field, is marked in the field. If the area of the square plot is $k {\mathrm{m}}^2$, find the value of $k$. $\left(\mathrm{Take} \mathrm{\pi }=\frac{22}{7}\right)$

The inside perimeter of a practice running track with semicircular ends and straight parallel sides is $312 \mathrm{m}$. The length of the straight portions of the track is $90 \mathrm{m}$. If the track has a uniform width of $2 \mathrm{m}$ throughout, find its area.

The boundary of the shaded region in the given figure consists of three semicircular arcs, the smaller ones being equal. If the diameter of the larger arc is $10 \mathrm{cm}$, calculate the area of the shaded region. Use $\left(\mathrm{\pi }=3.14\right)$

If the area of the region between two concentric circles given in the figure is $k {\mathrm{cm}}^2$, where the length of the chord of the outer circle touching the inner circle is $14 \mathrm{cm}$, then find the value of $k$. Use $\left(\mathrm{\pi }=\frac{22}{7}\right)$

The figure shows a circle with centre at $\mathrm{O}$ and $\angle \mathrm{AOB} = 90°$. If the radius of the circle is $40 \mathrm{cm}$, the area of the shaded portion of the circle is $k {\mathrm{cm}}^2$, find the value of $k$ (Take $\mathrm{\pi }= 3.14$).

$\mathrm{ABCD}$ is a flower bed. If $\mathrm{OA}=21 \mathrm{m}$ and $\mathrm{OC}=14 \mathrm{m}$, then the area of the bed is $k {\mathrm{m}}^2$, find the value of $k$. (Use $\mathrm{\pi }=\frac{22}{7}$).

 In the given figure$\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are centres of equal circles which touch externally in pairs and $\mathrm{ABCD}$ is a square of side $14 \mathrm{cm}$. If the area of the shaded region is $k {\mathrm{cm}}^2$, find the value of $k$. Use $\left(\mathrm{\pi }=\frac{22}{7}\right)$