Question

A farmer has to plough the field for five different types of crops naming $A,B,C,D$ and $E$ in a circular field. If the diameter of the field, where crops $A,B$ and $C$ are grown is 126 units and every other band is 21 units wide. Then, choose the correct option.

i) Area of region, where crop $A$ is grown $=1386$ sq. units
ii) Area of region, where crop $B$ is grown $=22176$ sq. units
iii) Area of region, where crops $A,B,C$ and $D$ are grown $=5544$ sq. units
iv) Area of region, where crop $E$ is grown $=34650$ sq. units

• A. i) only
• B. ii) and iii) only
• C. ii), iii) and iv)
• D. i), ii) and iii)

Answer 1

The correct option is A

i) only

Diameter of the region, where crops $A,B$ and $C$ are grown $=126$ units
$\therefore$ Radius of the region $=\frac{126}{2}=63$ units
Width of each band $=21$ units

i.) Radius of the region, where crop A is grown $=\frac{42}{2}=21$ units
Area of the region, where crop $A$ is grown $=\pi r^2=\frac{22}{7}\times 21\times 21$
$=1386$ sq. units

ii) Radius of the region, where crop $B$ is grown $=21+21=42$ units
$\therefore$ Area of the region, where crop $B$ is grown $=\frac{22}{7}\times 42\times 42-\frac{22}{7}\times 21\times 21$
$=\frac{22}{7}({42}^2-{21}^2)=4158$ sq. units

iii) Radius of the regon, where crop $D$ is grown $=21\times 4=84$ units
$\therefore$ Area of the region where crops $A,B,C$ and $D$ are grown
$=\frac{22}{7}\times 84\times 84$
$=22176$ sq. units

iv) Radius of the region where crop $E$ is grown $=21\times 5=105$ units

$\therefore$ Area of the region, where crop $E$ is grown $=\frac{22}{7}\times 105\times 105-$ Area of the region where crops $A,B,C$ and $D$ are grown

$=34650-22176$
$=12474$ sq. units