Question

please answer the question​

Answer 1

Answer:

(a) the area of the remaining sheet is 536cm^2

Answer 2

Question -:

• a ) From a circular card sheet of radius 14 cm two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in figure) . Find the area of the remaining sheet .

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Given :

• Radius of big circle (R) = 14cm
• radius of small (r) = 3.5cm
• Length of rectangle = 3cm
• Breadth of rectangle= 1cm

Need To Find :

• Area of Remaining sheet .

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Solution:−

$\underline {\boxed {\sf{ Area\ of\ rectangle= Length\times breadth}}}\\ \\ \underline {\boxed {\sf{Area\ of\ circle = \pi r^2}}}$

⠀⠀⠀⠀⠀We have to find the Area of remaining sheet

Now ,

$:\implies\sf\ Remaining\ Area= \pi R^2-(2\pi r^2+\ell \times b)\\ \\ \\ :\implies\sf\ Area= \dfrac{22}{\cancel{7}}\times 14\times \cancel{14}-\Big(2\times \dfrac{22}{\cancel{7}}\times \cancel{3.5}\times 3.5+ 3\times 1\Big)\\ \\ \\ :\implies\sf\ Remaining\ Area= 22\times 14\times 7-\Big( 2\times 0.5\times 3.5\times22 +3\Big)\\ \\ \\ :\implies\sf\ Remaining\ Area=616 -\Big(77+3\Big)\\ \\ \\ :\implies\sf\ Remaining\ Area= 616-80\\ \\ \\ :\implies\underline{\boxed{\sf\ Remaining\ Area=536cm^2}}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Area \:of\:Remaining \:sheet\:is\:\bf{536\: cm^{2}}}}}$

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Question -:

• b ) How many times will wheel of radius 14cm have to rotate to cover a distance of 22 metre .

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Given :

• The Radius of Wheel (r) is 14 cm .
• The Distance need to cover is 22 m .

Need To Find :

• How many Rotation will take to cover Given distance.

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Solution -:

$:\underline {\boxed {\sf{ Circumference \ of\ Circle = Distance \:Covered \;in\;1 \:rotation }}}$

⠀⠀⠀⠀⠀We have to find how many Rotation will it take to cover 22 m or 2200 cm [ 1 m = 100 cm ]

As , We know that ,

• $\underline {\boxed {\sf{ Perimeter \ of\ circle = 2\pi r}}}$

Now ,

$:\implies\sf\ \ Circumference =2 \pi R \\ \\ \\ :\implies\sf\ Circumference = 2 \times \dfrac{22}{\cancel{7}}\times \cancel{14}\\ \\ \\ :\implies\sf\ \ Circumference = 2 \times 22 \times 2 \\ \\ \\ :\implies\sf\ \ Circumference= 44 \times 2 \\ \\ \\ :\implies\underline{\boxed{\sf\ Circumference \ =88cm}}$

As, We know that ,

$:\underline {\boxed {\sf{ Circumference \ of\ Circle = Distance \:Covered \;in\;1 \:rotation }}}$

Therefore,

• Distance Covered in 1 rotation = 88 cm

⠀⠀⠀⠀⠀We have to find how many Rotation will it take to cover 22 m or 2200 cm

$\underline {\boxed {\sf{ No. \:of \:Rotation = \dfrac{Distance \:Need\:To\:Cover\:}{Distance \:in\:1\:Rotation}}}}$

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

$:\implies \sf{ No. \:of \:Rotation = \dfrac{2200\:}{88}}\\\\ :\implies\sf{No.\:of\:Rotations\:= \:25}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Number \:of\:Rotation \:is\:\bf{25\:} }}}$

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