Kesab Chandra Nag Solutions for Exercise 1: EXERCISE-3

$3.6$ quintal paddy is produced in a rectangle of size $28 \mathrm{m} \times 24 \mathrm{m}.$ In the same rate, the quantity of paddy produced in a circular field is $5280 \mathrm{kg}.$ Find the diameter of the circular field in $\mathrm{m}$.

There is a circular bunker around a fort. If the breadth of the bunker be $700 \mathrm{cm}$ and its area be $29.411 \mathrm{sq}-\mathrm{m},$ then find the area of the fort in ${\mathrm{m}}^2$.

The area of a circle is $616 \mathrm{sq}-\mathrm{m}.$ Find the area and perimeter of the square inscribed in it.

The diameter of a circular house is $62 \mathrm{m}$ and the breadth of its wall is $2 \mathrm{m}.$ Find the area of the wall in ${\mathrm{m}}^3$.
(Write the approximate answer up to one decimal point)

The diameter of a circular grass-field is $40 \mathrm{m}$. There is a road of breadth $1 \mathrm{m}$ starting from $1 \mathrm{m}$ away of its end point. calculate the expenditure to grass the road at a rate of $28$ paisa per sq-m.

The length and breadth of a rectangle inscribed in a circle are $8 \mathrm{cm}$and $6 \mathrm{cm}$ respectively. Find the area of the circle in $\mathrm{sq}-\mathrm{cm}$.
(Express the result in decimal form and use $\mathrm{\pi }=3.14$)

Each of the sides of an equilateral triangle is $a \mathrm{cm}.$ Find the ratio of the areas of its circumcircle and incircle.

If a square is inscribed in a circle is $64 \mathrm{sq}-\mathrm{cm}.$ Find the area of the circle in $\mathrm{sq}-\mathrm{cm}$.