Question

The circumference of a given circular park is $55$ m. It is surrounded by a path of uniform width $35$ cm. Find the area of the path.

• A. $23.125m^2$
• B. $19.635m^2$
• C. $17.245m^2$
• D. $27.155m^2$

Answer 1

The correct option is B $19.635m^2$

Circumference of circular park $=55$ m

$2\pi r=55$ m

$\Rightarrow r=\frac{7}{2\times 22}\times 55=\frac{35}{4}$

Area of this field:

$\pi \times r^2=\pi \times {\left(\frac{35}{4}\right)}^2=240.625m^2$

A uniform width path is there in surrounding this circular field.

Width $=0.35$ m

Radius increased by $0.35$ m

Now new radius will be $R=0.35+\frac{35}{4}=\frac{910}{100}$ cm

New Area $=\pi \times {\left(\frac{910}{100}\right)}^2=260.26m^2$

Area of extended path:

$A=260.26-240.625=19.635m^2$