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 is 210 units and every band is 21 units wide. Then, mark the incorrect option.

I.Area of region, where crop A is grown = $1386unit{s}^2$
II. Area of region, where crop B is grown = $22176unit{s}^2$
III.Area of region, where crops A,B,C and D are grown = $5544unit{s}^2$
IV. Area of region, where crop E is grown = $34650unit{s}^2$.

• A. I,II
• B. II, III
• C. II, III, IV
• D. I, II, III

Answer 1

The correct option is C

II, III, IV

Diameter of field = 210 units
$\therefore$ Radius of field = 105 units
Width of each band = 21 units

I. Radius of the region, where crop A is to be grown
$=105-4\times 21$
= 105 - 84 = 21 units
Area of the region, where crop A is to be grown = $\pi r^2=$ $\frac{22}{7}\times 21\times 21$
= 1386 sq units

II. Radius of the region, where crops A and B are to be grown
$=105-3\times 21$ = 42 units
$\therefore$ Area of the region, where crops A and B are to be grown
$\frac{22}{7}\times 42\times 42$
= 5544 sq units.

Or, Area of the region, where crop B is to be grown
= 5544 - 1385
= 4158 sq units

III. Radius of the region, where crops A,B,C are D are to be grown
= 105 - 21 = 84 units
$\therefore$ Area of the region:
$=\frac{22}{7}\times 84\times 84$
= 22176 sq units

IV. Area of the region, where crop E is to be grown $=\frac{22}{7}\times 105\times 105-22176\left(Areaof3rdregion\right)$
= 12474 sq units