Question

from a circular card sheet of radius 14cm two circle of radius 3.5cm and breadth 1 cm are removed (as shown in the adjoining figure) find the area of remaining sheet​

Answer 1

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Area of outer circle =$\pi {r}^{2} \\ = \frac{22}{7} \times 14 \times 14 \\ = 22 \times 28 = 616 cm²</p><p>⠀⠀⠀⠀</p><p>\\ \\ area \: of \: inner \: circle \: = 2 \times \pi {r}^{2} \\ \: = \: 2 \times \frac{22}{7} \times 35 \times 35 \\ = 22 \times 3.5 \\ = 77 {cm}^{2} \\ \\ </p><p>area \: of \: rectangle = \: l \times b \\ area</p><p> \: of \: whole \: circle \: -</p><p> \: ( \: area </p><p>\: of \: the</p><p> \: both \: circles \: </p><p>+ </p><p>\: area \: of</p><p> \: rectangle</p><p> \: ) \: = \: area </p><p>\: of</p><p> \: remaing \: sheet. \\ = 616 \: - \: ( \: 77 + 3) \\</p><p> = 616 - 80 = </p><p> {536cm}^{2} ....$

Answer 2

✧ Given:

• Radius of circular sheet = 14cm
• Radius of Small circle = 3.5cm
• Length of Rectangle = 3cm
• Breadth of Rectangle = 1cm
• R denotes Radius
• π denotes 22/7

⠀⠀

✧ To Attain:

• Area of Circular card
• Area of small Circle
• Area of 2nd Small circle
• Area of Rectangle
• Area of Remaining sheet

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✧ Explanation:

The Question says that there is circular sheet whose radius is 14cm and in this circle there are 2 more small circles having radius 3.5cm. After there is a Rectangle of length 3cm and Breadth 1 cm are removed then we are asked to find the area that has been remained in the circle! by using the formula of Area of Circle, we have our result. So, let's find out explainly•

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✧ Solution:

Area of Circular Card = πr²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf\dfrac{22}{7}\:\times~14\:\times~14$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 616cm²

⠀⠀⠀⠀

Area of Small Circle = πr²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=$\sf\dfrac{ \cancel{22}}{ \cancel{7}}\:\times~ \dfrac{ \cancel{35}}{ \cancel{10}} \:\times~ \dfrac{35}{10}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 38.5cm²

⠀⠀⠀⠀

Area of 2nd Small circle = 38.5cm²

⠀⠀⠀⠀

Area of Rectangle = Length × Breadth

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3 × 1

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3cm²

⠀⠀⠀⠀

Area of Remaining sheet = 616 - (38.5+38.5+3)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 616 - 80

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 536cm²

⠀⠀⠀⠀

$\therefore \: { \underline{ \sf{Area \: of \: Remaining \: sheet \: is \: \pmb{536cm}^{2} }}}$