Question

The diameter of the circular garden is 42 m. There is a 3.5 m wide road around the garden. Find the area of the road.

Answer 1

Given,

The diameter of the circular garden is 42 m.

$\Rightarrow$ Radius of the circular garden (r) $=\frac{42}{2}=21$ m

Width of the road = 3.5 m

So, radius of the outer circle (R) = radius (r) + width of the road

= 21 + 3.5= 24.5 m

Area of the road = area of outer circle – area of circular garden

$=\pi R^2–\pi r^2$

$=\pi (R^2–r^2)$

$=\frac{22}{7}\left[\right(24.5{)}^2–\left(21{)}^2\right]$

$=\frac{22}{7}(24.5+21)(24.5–21)$ [As $a^2-b^2=(a+b)(a-b)]$

$=\frac{22}{7}\times 45.5\times 3.5$

$=22\times 45.5\times 0.5$

= 500.50 sq. m

Therefore, the area of the road is 500.50 sq. m.