Question

from a circular sheet of radius 8cm, a circular sheet of radius 6cm is removed find the area of remaining sheet​

Answer 1

Given : From a circular sheet of radius 8cm, a circular sheet of radius 6cm is removed .

Need To Find : The area of Remaining sheet.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❒ Finding Area of Remaining sheet :

$\underline {\frak{ As,\:We\:Know\:that\:,}}$

⠀⠀⠀⠀⠀ $\implies {\underline {\sf{ Area _{(Circle)} = \pi \times r^{2} \:units .}}}$

⠀⠀⠀⠀⠀Here r is the Radius of Circle and $\pi=\dfrac{22}{7}$ .

Given that ,

• From a circular sheet of radius 8cm, a circular sheet of radius 6cm is removed .

❍ Let's Consider R be the radius of bigger Circle orbwhole sheet and r be the radius of smaller Circle.

Then ,

⠀⠀⠀⠀⠀$\boxed{\sf{Area \:of\:Remaining \:Sheet\:=Area \:of\:bigger \:Circle \:_{(Whole\:Sheet)} - Area\:of\:Smaller\:Circle _{(Removed\:Sheet)}\:}}$

Or ,

⠀⠀⠀⠀⠀$\boxed{\sf{Area \:of\:Remaining \:Sheet\:=\pi R^{2} - \pi r^{2}\:}}$

⠀⠀⠀⠀⠀$\boxed{\sf{Area \:of\:Remaining \:Sheet\:=\pi( R^{2} - r^{2})\:}}$

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀⠀$\longmapsto { \tt{ Area\:of\:Remaining \:sheet\: =\pi ( 8 ^{2} - 6^{2}) }}$

⠀⠀⠀⠀⠀⠀$\longmapsto { \tt{ Area\:of\:Remaining \:sheet\: =\pi ( 64 - 36 ) }}$

⠀⠀⠀⠀⠀⠀$\longmapsto { \tt{ Area\:of\:Remaining \:sheet\: =\pi ( 28 ) }}$

As , We know that ,

$\star\pi \:= \dfrac{22}{7}$

⠀⠀⠀⠀⠀⠀$\longmapsto { \tt{ Area\:of\:Remaining \:sheet\: =\dfrac{22}{\cancel {7}}\times \cancel {28} }}$

⠀⠀⠀⠀⠀⠀$\longmapsto { \tt{ Area\:of\:Remaining \:sheet\: =\:22\times 4 }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  Area\:of\:Remaining \:Sheet\:= 88\: cm^{2}}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline { \mathrm {  Area\:of\:Remaining \:Sheet\:is\: 88\: cm^{2} }}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀