Question

A circular path runs around a circular field ,the outer perimeter is 88 m and inner perimeter is 22m less than the outer perimeter .The area of the path

Answer 1

$\underline{\mathfrak{\huge{Question:}}}$

A circular path runs around a circular field. The outer perimeter is 88 m and inner perimeter is 22m less than the outer perimeter . What will be the area of the path ?

$\underline{\mathfrak{\huge{Answer:}}}$

Let the Outer Radius = R
Inner Radius = r

Outer Perimeter = 88 m

Perimeter of a circle = Circumference of the circle

=》 Outer Circumference = 88 m

=》 $2 \pi R$ = 88

=》 R = $\frac{88 \times 7}{2 \times 22}$

=》 $\boxed{\tt{R = 14 m}}$

Inner Perimeter = 88 - 22 ( m )

=》 Inner Circumference of the circle = 88 - 22 ( m )

=》 Inner Circumference = 66 m

=》 $2 \pi r$ = 66

=》 r = $\frac{66 \times 7}{2 \times 22}$

=》 $\boxed{\tt{r = 10.5 m}}$

Area of the Path = Area of the Outer Circle - Area of the Inner Circle

=》 Area of the Path = $2 \pi (R^{2} - r^{2})$

=》 Area = $2 \times \frac{22}{7} \times (14^{2} - 10.5^{2})$

=》 Area = $2 \times \frac{22}{7} \times 85.75$

=》 $\boxed{\tt{Area\:of\:the\:path = 539\:m^{2}}}$