Question

From a circular card sheet of radius 14cm , two circles of radius 3.5cm and a rectangle of length

3cm and breadth 1cm are removed find the area of the remaining sheet.​

Answer 1

$\underline{\sf\ Solution:-}$

Area of remaining sheet = Area of whole -(Area of 2 circles + Area of rectangle)

$:\implies\sf\ Area\ of\ rectangle= Length\times breadth\\ \\ \\ :\implies\sf\ Area\ of\ circle = \pi r^2$

Given :-

Radius of big circle (R) = 14cm

radius of small (r) = 3.5cm

Length of rectangle = 3cm

Breadth of rectangle= 1cm

• We have to find the Area of remaining sheet

Now ,

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

Answer 2

Answer:

Given :-

• A circular card sheet of radius 14 cm, two circles of radius is 3.5 cm and a rectangle of length is 3 cm and breadth 1 cm are removed.

To Find :-

• What is the area of remaining sheet.

Formula Used :-

$\sf\boxed{\bold{Area\: of\: Circle =\: {\pi}{r}^{2}}}$

$\sf\boxed{\bold{Area\: of\: Rectangle =\: Length \times Breadth}}$

Solution :-

Given :

• Radius of circular sheet (R) = 14 cm
• Radius of smaller circle (r) = 3.5 cm
• Length of rectangle = 3 cm
• Breadth of rectangle = 1 cm

According to the question by using the formula we get,

↦ Area of remaining sheet = Area of circular sheet - (Area of two smaller circle + Area of rectangle)

$\implies \sf Area\: of\: remaining\: sheet =\: {\pi}{R}^{2} - 2({\pi}{r}^{2} + length \times breadth)$

$\implies \sf Area\: of\: remaining\: sheet =\: \dfrac{22}{7} \times {(14)}^{2} - 2 \times \dfrac{22}{7} \times {(3.5)}^{2} + 3 \times 1$

$\implies \sf Area\: of\: remaining\: sheet =\: \dfrac{22}{\cancel{7}} \times 14 \times {\cancel{14}} - 2 \times \dfrac{22}{\cancel{7}} \times {\cancel{3.5}} \times 3.5 + 3$

$\implies \sf Area\: of\: remaining\: sheet\: =\: 22 \times 14 \times 2 - (44 \times 0.5 \times 3.5 + 3)$

$\implies \sf Area\: of\: remaining\: sheet\: =\: 616 - 80$

$\implies \sf\bold{\red{Area\: of\: remaining\: sheet =\: 536\: {cm}^{2}}}$

$\therefore$ The area of remaining sheet is 536 cm² .