Question

Find the area and circumference of the circle when (a) the radius is 7 cm, and (b) diameter is

28 cm. (Take π​

Answer 1

1) Radius of the circle is 7 cm.

• Area of the circle = 154 cm².
• Circumference of the circle = 44 cm.

2) Diameter of the circle is 28 cm.

• Area of the circle = 616 cm².
• Circumference of the circle = 88 cm.

To Find :

The area and the circumference of the circle.

When,

1. Radius = r = 7 cm.
2. Diameter = d = 28 cm.

Solution :

1) When the radius of the circle is 7 cm.

★ Area of the circle.

We know that,

$\orange{ \bullet} \: \: \sf area \: of \: the \: circle \: = \pi {r}^{2}$

$:\implies \rm \dfrac{22}{7} \times {(7 \: cm)}^{2} \\ \\ :\implies \rm \dfrac{22}{ \not{7}} \times 7 \: cm \times \not{7 \: cm} \\ \\ :\implies \rm 22 \times 7 \: {cm}^{2} \\ \\ :\implies \rm 154 \: {cm}^{2}$

Hence, the area of the circle when radius is 7 cm is 154 cm².

_____________________

★ Circumference of the circle.

We know that,

$\orange{ \bullet} \: \: \sf circumference \: of \: the \: circle = 2\pi r$

$:\implies \rm 2 \times \dfrac{22}{ \not{7}} \times \not{7 \: cm} \\ \\ :\implies \rm 2 \times 22 \: cm \\ \\ :\implies \rm 44 \: cm$

Hence, the circumference of the circle when radius is 7 cm is 44 cm.

Hence,

The area and the circumference when the diameter is 28 cm are 154 cm² and 44 cm.

________________________________

2) When diameter of the circle is 28 cm.

First we need to find the radius of the circle.

We know that,

$\red{ \bullet} \: \: \sf radius = \dfrac{diameter}{2} \\ \\ :\implies \rm \dfrac{ \not{28}}{ \not{2}} \: cm \\ \\ :\implies \rm 14 \: cm$

★ Area of the circle.

We know that,

$\orange{ \bullet} \: \: \sf area \: of \: the \: circle \: = \pi {r}^{2}$

$:\implies \rm \dfrac{22}{7} \times {(14 \: cm)}^{2} \\ \\ :\implies \rm \dfrac{22}{ \not7} \times 14 \: cm \times \not{14 \: cm} \\ \\ :\implies \rm 22 \times 14 \times 2 \: {cm}^{2} \\ \\ :\implies \rm 22 \times 28 \: {cm}^{2} \\ \\ :\implies \rm 616 \: {cm}^{2}$

Hence, the area of the circle when diameter is 28 cm is 616 cm².

____________________

★ Circumference of the circle.

$\orange{ \bullet} \: \: \sf circumference \: of \: the \: circle = 2\pi r$

$:\implies \rm 2 \times \dfrac{22}{ \not{7}} \times \not{14 \: cm} \\ \\ :\implies \rm 2 \times 22 \times 2 \: cm \\ \\ :\implies \rm 4 \times 22 \: cm \\ \\ :\implies \rm 88 \: cm$

Hence, the circumference of the circle when the diameter is 28 cm is 88 cm.

Hence,

The area and the circumference when the diameter is 28 cm are 616 cm² and 88 cm.