Question

find the radius of a circular field whose area is 154 cm2​

Answer 1

• The radius of a circular field = 7 cm.

Given :

• Area of a circular field = 154 cm²

To Find :

• The radius of a circular field.

Solution :

We know that,

$\blue{\boxed{ \sf{ \orange{Area \: Of \: A \: Circular \: Field = \pi {r}^{2} }}}}$

Where,

$\bullet \: \: \rm r = Radius$

Given,

$\rm Area \: of \: a \: circular \: field = 154 \: {cm}^{2}$

That means,

$\rm\pi {r}^{2} = 154 \: {cm}^{2}$ –––(1)

Where,

$\bullet \: \: \rm \pi = \dfrac{22}{7}$

Substitute the value of π in equation (1),

$: \implies \rm\dfrac{22}{7} \times {r}^{2} = 154 \: {cm}^{2} \\ \\ : \implies \rm {r}^{2} =154 \: {cm}^{2} \times \dfrac{7}{22} \\ \\ : \implies \rm {r}^{2} = 77 \times \frac{7}{11} \: {cm}^{2} \\ \\ : \implies \rm {r}^{2} = 7 \times 7 \: {cm}^{2} \\ \\ : \implies \rm {r}^{2} = 49 \: {cm}^{2} \\ \\ : \implies \rm r = \sqrt{49 \: {cm}^{2} } \\ \\ : \implies \rm r = 7 \: cm \\ \\ \: \: \: \therefore \: \: \rm r = 7 \: cm$

Hence,

The radius of a circular field is 7 cm.

Verification :

Given,

• Area of a circular field = 154 cm²

We know that,

Area of circular field = πr²

Now we have,

$\bullet \: \: \rm \pi = \dfrac{22}{7} \\ \\ \bullet \: \: \rm r = 7 \: cm$

Substitute both the values in equation (1),

$: \implies \rm \dfrac{22}{7} \times {(7 \: cm)}^{2} = 154 \: {cm}^{2} \\ \\ : \implies \rm\dfrac{22}{7} \times 49 \: {cm}^{2} = 154 \: {cm}^{2} \\ \\ : \implies \rm 22 \times 7 \: {cm}^{2} = 154 \: {cm}^{2} \\ \\ : \implies \rm 154 \: {cm}^{2} = {154 \: cm}^{2}$

Hence Verified !