Question

The inner circumference of a circular track is 242 metre the track is uniformly 7 metre wide find the area of the track

Answer 1

Given :-

• Inner Circumference = 242 m
• Width of the track = 7 m

To Find :-

• Area of the truck

Solution :-

Radius of the circle :-

$:\implies\:\sf{ 2 \pi r=242}$

$:\implies\:\sf{ 2 \times \dfrac{22}{7} \times r=242}$

$:\implies\:\sf{ \dfrac{7}{44} \times r=242}$

$:\implies\:\sf{r= \dfrac{7}{44} \times 242}$

$:\implies\:\sf{r= \dfrac{7}{2} \times 11}$

$:\implies\:\sf{r= \dfrac{77}{2} }$

$:\implies\:\sf\pink{r= 38.5\:m }$

Hence,

Inner Radius = 38.5 m

Outer radius of the circle :-

$:\implies\:\sf{Inner\:Radius +Width \:of\:the\:track}$

$:\implies\:\sf{38.5 +7}$

$:\implies\:\sf\blue{45.5 \:m}$

Area along with the track :-

$:\implies\:\sf{\pi r^2}$

$:\implies\:\sf{\dfrac{22}{7}\times 45.5 \times 45.5 }$

$:\implies\:\sf{45545.\:\dfrac{5}{7} }$

$:\implies\:\sf\blue{6506.5 \:m^2 }$

Area without track :-

$:\implies\:\sf{\pi r^2}$

$:\implies\:\sf{\dfrac{22}{7}\times 38.5 \times 38.5 }$

$:\implies\:\sf{32609.\:\dfrac{5}{7} }$

$:\implies\:\sf\purple{4658.5\:m^2}$

Area of the track :-

$:\implies\:\sf{Area\:along\:with\:track-Area\:without\:track }$

$:\implies\:\sf{6506.5-4658.5 }$

$:\implies\:\sf\purple{1848\:m^2 }$

Therefore,

Area of the track = 1848 m²

Answer 2

$\Huge{\textbf{\textsf{{\color{navy}{A}}{\purple{nsw}}{\pink{er}}{\color{pink}{:}}}}}$

Circumference of the inner circle=2πr=24π =>r=12m

Radius of the outer circle =14m

Therefore, circumference of the outer circle =2π(14)

=2×22

=88m

(Assuming π= 7).

OR

Circumference of the inner circle=2πr=24π

=>r=12m

Radius of the outer circle =14m

Therefore, circumference of the outer circle

=2π(14)

=2×22

=88m