Question

if the circumference of the circle sheet is 154 m, find its radius. Also find the area of the sheet . { Take π = 22/7​

Answer 1

circumference of circle =2πr

154 = 2×(22/7)r

r = 24.5 cm

Area of circle = πr²

area of circle = 22/7×(24.5)² =1884.785 m²

Answer 2

Answer :

• Radius = 24.5 m
• Area = 1886.5 m²

Step-by-step explanation :

To Find,

• The radius of the circular sheet
• The area of the sheet

Solution,

Given that,

Circumference of the circular sheet = 154 m

• Therefore, Radius of the sheet

We know that,

$\underline{ \boxed{ \bf{Circumference \: \: of \: \: a \: \: circle = 2\pi \: r}}}$

$\sf{ \mapsto \: 154 = 2 \times \dfrac{22}{7} \times r}$

$\sf{ \mapsto \: 154 = \dfrac{2 \times 22}{7} \times r}$

$\sf{ \mapsto \: 154 = \dfrac{44}{7} \times r}$

$\sf{ \mapsto \: r = 154 \times \dfrac{7}{44}}$

$\sf{ \mapsto \: r = 77\times \dfrac{7}{22}}$

$\sf{ \mapsto \: r = 7\times \dfrac{7}{2}}$

$\sf{ \mapsto \: r = \dfrac{49}{2}}$

$\sf{ \mapsto \: r = 24.5m} \: \: \bigstar$

Therefore, Radius of the circular sheet is 24.5 m

• The area of the sheet

We know that,

$\underline{ \boxed{ \bf{Area \: \: of \: \: the \: \: circle= \pi\: {r}^{2}}}}$

$\sf{ \mapsto \: \dfrac{22}{7} \times {(24.5)}^{2} }$

$\sf{ \mapsto \: \dfrac{22}{7} \times 24.5 \times 24.5}$

$\sf{ \mapsto \: 22 \times 3.5 \times 24.5}$

$\sf{ \mapsto \: 77 \times 24.5}$

$\sf{ \mapsto \: \: 1886.5 \: {m}^{2}} \: \: \bigstar$

Therefore,the area of the circular sheet is 1886.5 m²