Question

please solve this question​

Answer 1

$area = \pi \: {r}^{2}$

153.86= 3.14 x r^2 (Dividing by 3.14)

49 = r^2

$r = \sqrt{49}$

r=7 cm

Answer 2

${\large{\boxed{\underline{\mathrm{\orange{Given:-}}}}}}$

• Area of the circular field = 153.86 cm²

${\large{\boxed{\underline{\mathrm{\red{To \ Find:-}}}}}}$

• Radius of the circle

${\large{\boxed{\underline{\mathrm{\pink{Formula \ Used:-}}}}}}$

${\pink{\bigstar}} \ {\boxed{\tt{\green{Area \ of \ a \ Circle = \pi r^2}}}} \ {\pink{\bigstar}}$

where,

• r = Radius
• ${\bf{\pi}}$ = 3.14

${\large{\boxed{\underline{\mathrm{\blue{Solution:-}}}}}}$

According to the question by using the formula of Area of a Circle, we get,

$: \ \Longrightarrow \ {\sf{\pink{3.14r^2 = 153.86 \ cm^2}}}$

Solving the above equation,

$: \ \Longrightarrow \ {\sf{r^2 = \dfrac{153.86}{3.14} \ cm^2}}$

$: \ \Longrightarrow \ {\sf{r^2 = \dfrac{{\cancel{153.86}}}{{\cancel{3.14}}} \ cm^2}}$

$: \ \Longrightarrow \ {\sf{r^2 = 49 \ cm^2}}$

$: \ \Longrightarrow \ {\sf{r = {\sqrt{49 \ cm^2}}}}$

$: \ \Longrightarrow \ {\sf{r = 7 \ cm}}$

$: \ \Longrightarrow \ {\underline{\boxed{\blue{\sf{Radius = 7 \ cm}}}}}$

${\red{\therefore}} \ {\boxed{\green{\mathsf{Radius \ is \ {\underline{\bf{7 \ cm}}}}}}}$

${\huge{\green{\checkmark}}} \ {\large{\boxed{\underline{\mathrm{\bf{\orange{Verification:-}}}}}}} \ {\huge{\green{\checkmark}}}$

$: \ \Longrightarrow \ {\sf{3.14 \times 7^2 = 153.86 \ cm^2}}$

$: \ \Longrightarrow \ {\sf{3.14 \times 7 \times 7 = 153.86 \ cm^2}}$

$: \ \Longrightarrow \ {\sf{3.14 \times 49 = 153.86 \ cm^2}}$

$: \ \Longrightarrow \ {\sf{153.86 \ cm^2 = 153.86 \ cm^2}}$

$\Longrightarrow {\bf{\red{LHS = RHS}}} \Longleftarrow$

${\sf{\pink{Hence,}}} \ {\sf{\green{Verified}}} \ {\large{\green{\checkmark}}}$