Question

From a circular card sheet of radius 14cm , two circle of radius3.5cm and a rectangle of length 3cm and breadth 1cm are removed ( as shown in the adjoining figure).Find the area of the remaining sheet. *​

Answer 1

Given,

A circular card sheet of radius 14cm with 2 circles of radius 3.5cm and a rectangle of length 3cm and breadth 1cm are removed.

To Find,

The area of the remaining sheet.

Solution,

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-1.5,-1)(-1.5,-1)(-1.5,-1.5)\qbezier(-1.5,-1)(-1.5,-1)(1.25,-1)\qbezier(1.25,-1)(1.25,-1)(1.25,-1.5)\qbezier(1.25,-1.5)(1.25,-1.5)(-1.5,-1.5)\put(-1,0.5){\circle{.8}}\put(1,0.5){\circle{.8}}\end{picture}$

Radius of circular card sheet = 14 cm

Radius of each inner circle= 3.5 cm

Length of rectangle = 3 cm

Breadth of rectangle = 1 cm

In order to find the area of remaining sheet →

= Area of circular card sheet - (Area of 2 smaller circles + area of rectangle)

Area of circle = π$r^2$

Area of rectangle = lb

Substituting the values:

= $\dfrac{22}{7}  \times 14 \times 14 - (2 \times \dfrac{22}{7}   \times 3.5 \times 3.5) + 3 \times 1$

= 22 x 14 x 2 - [44×0.5×3.5+3]

= 616 - 80

= $536cm^2$

Therefore the area of the remaining sheet is $536cm^2$.

Note:

The symbol * refers to the multiplication symbol 'x'.

Formulas used:

→ Area of circle

→ Area of rectangle

Answer 2

Answer:

Step-by-step explanation:

Given,

A circular card sheet of radius 14cm with 2 circles of radius 3.5cm and a rectangle of length 3cm and breadth 1cm are removed.

To Find,

The area of the remaining sheet.

Solution,

Radius of circular card sheet = 14 cm

Radius of each inner circle= 3.5 cm

Length of rectangle = 3 cm

Breadth of rectangle = 1 cm

In order to find the area of remaining sheet →

= Area of circular card sheet - (Area of 2 smaller circles + area of rectangle)

Area of circle = π

Area of rectangle = lb

Substituting the values:

= 22 x 14 x 2 - [44×0.5×3.5+3]

= 616 - 80

=  

Therefore the area of the remaining sheet is .

Note:

The symbol * refers to the multiplication symbol 'x'.

Formulas used:

→ Area of circle

→ Area of rectangle