Question

A garden is surrounded by a circular path whose inner circumference is 264 m and
the outer circumference is 308 m. Find the width of the path.​

Answer 1

Question :

A garden is surrounded by a circular path whose inner circumference is 264 m and the outer circumference is 308 m. Find the width of the path.

Answer :

Given -

• Circumference of inner circle = 264 m
• Circumference of outer circle = 308 m

To find -

• Width of the path

Solution -

${\tt{Let \ the \ radius \ of \ inner \ circle \ be \ r_{1} \ and }}\\{\tt{ the \ radius \ of \ outer \ circle \ be \ r_{2}}}$

${\mathbb{\large{WE \ KNOW \ THAT}}}$

${\sf{\large{\blue{✯ \ Circumference \ = \ 2\pi {r}} }}}$

${\sf{\longmapsto \ Circumference \ of \ inner \ circle \ = \ 2\pi ({r _{1}) } }}$

${\sf{ \longmapsto \ 264 \ = \ 2\pi ({r _{1}) }}}$

${\sf{\longmapsto \ \frac{264}{2} \times \frac{1}{\pi} \ = \ ({r _{1}) }}}$

Now,

${\sf{\longmapsto \ Circumference \ of \ outer \ circle \ = \ 2\pi ({r _{2}) } }}$

${\sf{ \longmapsto \ 308 \ = \ 2\pi ({r _{2}) }}}$

${\sf{\longmapsto \ \frac{308}{2} \times \frac{1}{\pi} \ = \ ({r _{2}) }}}$

${\sf{\purple{ ♡ \ Width \ of \ path \ = \ r_{2} \ - \ r_{1}}}}$

${\sf{\hookrightarrow \ Width \ of \ path \ = \ ( \frac{308}{2} \times \frac{1}{\pi}) \: - \: ( \frac{264}{2} \times \frac{1}{\pi} ) }}$

(Taking common )

${\sf{\hookrightarrow \ Width \ of \ path \ = \ \frac{1}{2 \times \pi} (308 \times 264) }}$

${\sf{\hookrightarrow \ Width \ of \ path \ = \ \frac{7}{2 \times 22} \times 44 }}$

${\sf{\hookrightarrow \ Width \ of \ path \ = \ \frac{7}{\cancel{44}} \times \cancel{44} }}$

${\sf{\orange{ ✿\ Width \ of \ path \ = \ 7m}}}$

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@BrainlyFlash