Question

While making a mask,Riya removed two circles of radius 7 cm each and a rectangle of length 4 cm and breadth 1 cm from a circular card of radius 42 cm as shown in the adjoining figure.Find the area of the remaining card.​

Answer 1

AnswEr :

• Circle with Radius ( R ) = 42 cm
• Circle with Radius ( r ) = 7 cm
• Rectangle with Length 4 cm and Breadth 1 cm.
• Find Area of Remaining Card.

• According to the Question Now :

⇒ Area of Remaining Card = Area of Whole Circular Card - [Area of Rectangle + (2 Area of Circles)]

⇒ Area of Remaining Card = πR² - [(l × b) + 2 × (πr²)]

⇒ Area of Remaining Card = 22 /7 × ( 42 )² - [(4 × 1) + 2 × (22 /7 × ( 7 )²]

⇒ Area of Remaining Card = (22 × 6 × 42) - [4 + (2 × 22 × 7)]

⇒ Area of Remaining Card = 5544 - [4 + 308]

⇒ Area of Remaining Card = 5544 - 312

⇒ Area of Remaining Card = 5232 cm²

∴ Area of Remaining Card is 5232 cm².

Answer 2

$\bold{\Huge{\underline{\boxed{\sf{\red{ANSWER\::}}}}}}$

Given:

In a mask, Riya removed two circles of radius 7cm each and a rectangle of length 4cm and breadth 1cm from a circular card of radius 42cm as shown in the adjoining figure.

$\bold{\Large{\underline{\sf{\green{To\:find\::}}}}}$

The area of the remaining card.

$\bold{\Large{\underline{\sf{\purple{Explanation\::}}}}}$

We have,

• Two smaller circles of radius,[r]= 7cm
• Larger circular of radius,[R]= 42cm
• A rectangle of length,[l]= 4cm
• A rectangle of breadth,[b]= 1cm

A/q

• Area of larger circle:

We know that area of circle: πr²    [sq.units]

Radius of larger circle = 42cm

→ πR²

→ $\frac{22}{7} *42cm*42cm$

→ $\frac{22}{\cancel{7}} *\cancel{42}cm*42cm$

→ (22×6×42)cm²

→ 5544cm²

• Area of smaller circle:

→ πr²

→ $\frac{22}{7} *7cm*7cm$

→ $\frac{22}{\cancel{7}} *\cancel{7}cm*7cm$

→ (22×7)cm²

→ 154cm²

&

• Area of rectangle:

We know that area of rectangle: (length × Breadth)    [sq.units]

→ 4cm × 1cm

→ 4cm²

Now,

Remaining area= Ar. of larger circle - 2(Ar. of smaller circle)- area of rectangle

⇒ Remaining area= 5544cm² - 2(154cm²) - 4cm²

⇒ Remaining area= 5544cm² - 308cm² -4cm²

⇒ Remaining area= 5544cm² - 312cm²

⇒ Remaining area= 5232cm²

Thus,

The area of the remaining card is 5232cm².