R. D. Sharma Solutions for Chapter: Areas Related to Circles, Exercise 1: EXERCISE 13.1

Find the circumference and area of a circle of radius $4.2 \mathrm{cm}$.

A path of $4 \mathrm{m}$ width runs around a semi-circular grassy plot whose circumference is $163+\frac{3}{7} \mathrm{m}$. Find the cost of turfing the plot at the rate of $45 \mathrm{paise}$ per $\mathrm{sq}.\mathrm{m}$

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

A path of width $3.5 \mathrm{m}$runs around a semi-circular grassy plot whose perimeter is $72 \mathrm{m}$. Find the area of the path.                       

A circular pond is of diameter $17.5 \mathrm{m}$. It is surrounded by  $2 \mathrm{m}$ wide path .Find the cost of constructing the path at the rate of $₹25$ per square metre. $($Use $\mathrm{\pi }=3.14)$

The outer circumference of a circular race-track is $528 \mathrm{m}$. The track is everywhere $14 \mathrm{m}$ wide. Calculate the cost of leveling the track at the rate of $50 \mathrm{paise}$ $\mathrm{per} \mathrm{square} \mathrm{metre}$(Use $\mathrm{\pi }=\frac{22}{7})$.

A road which is $7 \mathrm{m}$ wide surrounds a circular park whose circumference is $352 \mathrm{m}$. Find the area of the road.

Prove that the area of a circular path of uniform width $\mathrm{h}$ surrounding a circular region $\mathrm{r}$ is $\mathrm{\pi h} (2\mathrm{r}+\mathrm{h})$.