Question

from a circular metal sheet of radius 9cm a circle of radius 4 cm is removed. find the area of the remaining sheet .take π3.14​

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• There's a circular metal sheet of radius 9 cm.
• A circular part of radius 4 cm is removed from it.
• The value of $\pi$ is 3.14

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The area of remaining metal sheet.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{(Circle)}=\pi{r}^{2}\:sq.units.}}}$

$\underline{\boxed{\sf{{Area}_{(Remaining\:sheet)}={Area}_{(Big\: circle)}-{Area}_{(Small\: circle)}\:sq.units.}}}$

${\underline{\underline{\bf{Solution:}}}}$

First, let's find the area of big circle i.e, the area of circular metal sheet.

$\:\:\:\:\:\implies{\sf{\pi{r}^{2}\:sq.units.}}$

$\:\:\:\:\:\implies{\sf{3.14\times {9}^{2}\:{cm}^{2}}}$

$\:\:\:\:\:\implies{\sf{3.14\times 81\:{cm}^{2}}}$

$\:\:\:\:\:\implies\underline{\bf{254.34\:{cm}^{2}}}$

The area of big circle is $\sf{254.34\:{cm}^{2}}$. So, now let's find the area of small circle i.e, the area of part which was cut out from the circular metal sheet.

$\:\:\:\:\:\implies{\sf{\pi{r}^{2}\:sq.units.}}$

$\:\:\:\:\:\implies{\sf{3.14\times {4}^{2}\:{cm}^{2}}}$

$\:\:\:\:\:\implies{\sf{3.14\times 16\:{cm}^{2}}}$

$\:\:\:\:\:\implies\underline{\bf{50.24\:{cm}^{2}}}$

Finally, the area of the remaining sheet:

$\:\:\:\:\:\implies{\sf{Area\:of\:big\:circle-Area\:of\:small\: circle}}$

$\:\:\:\:\:\implies{\sf{254.34-50.24\:{cm}^{2}}}$

$\:\:\:\:\:\implies\underline{\sf{\red{204.1\:{cm}^{2}}}}$

${\underline{\underline{\bf{Final\:answer:}}}}$

• The area of remaining metal sheet is 204.1 cm².

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