Question

From a Circular Card Sheet of Radius 14 cm, two circles of radius 3.5 cm and rectangle of length 3 cm and Breadth 1 cm are removed. Find the Area of the Remaining Sheet. (Take π
$= \frac{22}{7} )$
​

Answer 1

$\huge{\mathcal{\underline\green{Question}}}$

From a Circular Card Sheet of Radius 14 cm, two circles of radius 3.5 cm and rectangle of length 3 cm and Breadth 1 cm are removed. Find the Area of the Remaining Sheet. (Take π $= \frac{22}{7} )$

$\huge{\underline{\mathtt{\red{A} \pink{N} \green{S} \blue{W} \purple{E} \orange{R}}}}$

$\huge\boxed{\blue{Given :}}$

➣ Radius of Circular Card Sheet = 14 cm

➣ Two Circles and One Rectangle is cutted from the Circular Card Sheet

➣ Radius of 1st Circle = 3.5 cm

➣ Radius of 2nd Circle = 3.5 cm

➣ Length of the Rectangle = 3 cm

➣ Breadth of the Rectangle = 1 cm

$\huge\boxed{\red{To \: Find :}}$

➣ Area of The Remaining Sheet

$\huge\boxed{\pink {Solution :}}$

➪ Area of the Circular Card Sheet = πr²

⇒ Area of the Circular Card Sheet = $\frac{22}{7} \times 14 \times 14$

⇒ Area of the Circular Card Sheet = 616 cm²

$\:$

➪ Area of one small circle = πr²

⇒Area of one small circle = $\frac{22}{7} \times 3.5 \times 3.5$

⇒Area of one small circle = 38.8 cm²

$\:$

➪ Area of two small circles = 2 × 38.5 cm²

⇒Area of two small Circles = 77 cm²

$\:$

➪ Area of the Rectangle = length × breadth

⇒ Area of the Rectangle = 3 cm × 1 cm

⇒ Area of the Rectangle = 3 cm²

$\:$

➪ Total area to be removed = Area of 2 circles + Area of Rectangle

⇒ Total area to be removed = 77 cm² + 3 cm²

⇒ Total area to be removed = 80 cm²

$\:$

➪ Area of the Remaining Sheet = Area of Circle - Area to be removed

⇒Area of the Remaining Sheet = 616 cm² - 80 cm²

⇒Area of the Remaining Sheet = 536 cm²

➦ So, the area of the Remaining Sheet is 536 cm².

Answer 2

Answer:

Area of sheet =πr 2 = 22/7 ×14×14

=616cm 2

Area of 2 small circles =2×π×3.5×3.5

=77cm 2

Area of rectangle =3×1=3cm 2

Remaining Area =616−(77+3)

=536cm 2

.