Question

A gardener has to lay grass in a circular ground, leaving a space of $5m$ all around it. If the area of the ground with grass is $\frac{59400}{21}{m}^2$, find the area of the ground without grass. (Use $\pi =22/7$)

• A. $1022\frac{4}{7}sqm$
• B. $1022\frac{3}{7}sqm$
• C. $1021\frac{3}{7}sqm$
• D. $1021\frac{4}{7}sqm$

Answer 1

Answer: (C)

$1021\frac{3}{7}sqm$

Let radius of ground be $R$ $m$.

Now, $\pi r^2=\frac{59400}{21}{m}^2$

$\Rightarrow r^2=\frac{59400\times 7}{21\times 22}=900$

$\Rightarrow r=\sqrt{900}=30m$

$\therefore$ area of ground without grass $=\pi R^2-\frac{59400}{21}=\pi {(30+5)}^2-\frac{59400}{21}$

$=\frac{22}{7}\times 35\times 35-\frac{59400}{21}=3850-\frac{59400}{21}$

$=\frac{80850-59400}{21}=\frac{21450}{21}={1021}_7^3{m}^2$