Question

from a circular card sheet of radius 14 cm to circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed find the area of the remaining sheet

Answer 1

Hi

Ur answer is here

It is that there is a circle of radius 14cm.
If two circles of radius 3.5 cm radius and a rectangle of 3cm Length and 1 cm breadth are removed from the circle of 14 cm.
We have to find the rest area.....

So we will first calculate the area of two smaller circles + area of rectangle and we will subtract this area from the area of bigger circle....

So. area of bigger circle

$\pi \: r ^{2}$
$\frac{22}{7} \times {14}^{2}$
$= \frac{22}{7} \times 14 \times 14$
$= 22 \times 14 \times 2$
$= 22 \times 28 = 616$
So, the area of bigger circle is
$616 \: cm ^{2}$

Area of smaller circle .....

Radius = 3.5 cm

So.
using
$\pi {r}^{2}$
$\frac{22}{7 } \times 3.5 \times 3.5$
$= 22 \times 0.5 \times 3.5$
$= 11 \times 3.5 = 38.5$
$hence \: the \: area \: of \: smaller \: circle \\ \: is \: 38.5 {cm}^{2}$
It is given that there are two circles....
therefore, total area
= 38.5 × 2
$= 77 {cm}^{2}$

Area of rectangle ......

Length= 3 cm
Breadth = 1 cm

Area of square = l × b
So. 3 × 1
$= 3 {cm}^{2}$

Now. area of two circles and a rectangle
= area of two smaller circles + area of rectangle

$= 77 + 3 \\ = 80 {cm}^{2}$

So. If this area will be subtracted from the larger circle. We will get the required area

So.
$616 - 80 \\ = 536 {cm}^{2}$
Hence. the area of remaining sheet is
${536}^{2}$

Hope it helps......

Answer 2

the area of remaining sheet=536cm2