Question

find the area of circle ,given that =a diameter=42​

Answer 1

Answer:

1386

Step-by-step explanation:

area of circle=πr2

=22/7×21×21

=22/7×441

=22×63

=1386

Answer 2

Given,

The diameter of the circle is 42.

Then, the radius of circle = half of the diameter

That is, diameter/2 = 42/2 = 21

To find out,

The area of the circle.

Solution:

$Area \: of \: circle \: = \pi \: {r}^{2}$

$Area \: of \: circle \: = \frac{22}{7} \times 21 \times 21$

$Area \: of \: circle \: = 22 \times 3 \times 21$

$Area \: of \: circle \: = 1386 \: square \: units.$

Therefore the area of the circle is 1,386 square units.

Proof:

$Area \: of \: circle \: = \frac{22}{7} \times {r}^{2} \\ 1386 = \frac{22}{7} \times {r}^{2} \\ \frac{1386 \times 7}{21} = {r}^{2} \\ \frac{1386}{3} = {r}^{2} \\ 462 = {r}^{2} \\ r = \sqrt{462} \ \\r = approximately \: 21$

Additional information:

$Area \: of \: circle \: = \pi \: {r}^{2}$

$radius \: of \: circle \: = \sqrt{ \frac{area}{ \pi} }$

$diameter \: of \: circle \: = 2 r$

$circumference \: of \: circle \: = 2 \pi \: r$