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zzz [600]
2 years ago
14

Find the area of the region between two concentric circular paths. If the radii of the circular paths are 210 m. and 490 m. resp

ectively.​
Mathematics
1 answer:
taurus [48]2 years ago
6 0

Given :

  • The radii of the circular paths are 210 m. and 490 m.

To Find :

  • The area of the region between two concentric circular paths.

Solution :

Area of the outer circle :

\: \qquad  \dashrightarrow \sf{{ \pi \: \times  {(490)}^{2}  {m}^{2}}}

\: \qquad  \dashrightarrow \sf{{ \ \dfrac{22}{7} \times   \:490 \times 490 \:  {m}^{2}}}

\: \qquad  \dashrightarrow \sf{{ \ \dfrac{22}{ \cancel{7}} \times   \cancel{490} \times 490 \:  {m}^{2}}}

\: \qquad  \dashrightarrow \sf{{ \ {22} \times   70 \times 490 \:  {m}^{2}}}

\: \qquad  \dashrightarrow \bf{{ \ 754600 \:  {m}^{2}}}

⠀

Area of the inner circle :

\: \qquad  \dashrightarrow \sf{{ \pi \: \times  {(210)}^{2}  {m}^{2}}}

\: \qquad  \dashrightarrow \sf{{ \ \dfrac{22}{7} \times   \:210 \times 210 \:  {m}^{2}}}

\: \qquad  \dashrightarrow \sf{{ \ \dfrac{22}{ \cancel{7}} \times   \cancel{210} \times 210 \:  {m}^{2}}}

\: \qquad  \dashrightarrow \sf{{ \ {22} \times   30 \times 210 \:  {m}^{2}}}

\: \qquad  \dashrightarrow \bf{{ \ 138600 \:  {m}^{2}}}

⠀

Therefore,

Area of the region inside the circular paths :

\: \qquad  \dashrightarrow \sf{{ \ (754600 - 138600  )  \: {m}^{2}}}

\: \qquad  \dashrightarrow \bf{{ \ 616000 \:  {m}^{2}}}

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