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)

$\begin{gathered}:\implies\sf\ Area\ of\ rectangle= Length\times breadth\\ \\ \\ :\implies\sf\ Area\ of\ circle = \pi r^2 \end{gathered}$

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,

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

Answer 2

Answer:

Radius of the circular sheet= 14cm

Area=πr² =22 × 14 × 14cm²

_____

7

=616cm²

Area of 2 small circles=πr²

=2×22 × 3.5 × cm²

____

7

=77.0cm²

=Area of the rectangle= l × b

=3 × 1 cm² = 3cm²

Area of the remaining sheet after removing the 2 circles and 1 rectangle

=616 cm² - (77 + 3) cm²

=616 cm² - 80 cm² = 536 cm²

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