Question

A wire is in the form of a rectangle 18.7 cm long and 14.3 cm wide . if the wire is repeated and bent in the form of circle find the radius of and the area of the circle so formed​

Answer 1

Answer:

Step-by-step explanation:

perimeter of rectangle = (18.7+14.3)×2 = 33×2 = 66 cm

circumference of circle = perimeter of rectangle

2πr = 66

r = 66/2π

r = 66×7/2×22

r = 21/2

r = 10.5 cm

so,

radius of circle = 10.5 cm

Answer 2

★ CORRECT QUESTION ★

A wire is in the form of a rectangle 18.7 cm long and 14.3 cm wide .If the wire is reshaped and bent in the form of circle find the radius and the area of the circle so formed.

★ SOLUTION ★

• Length of the rectangle = 18.7 cm
• Breadth of the rectangle = 14.3 cm

Therefore,

Perimeter of the rectangle,

= 2( length + breadth)

= 2( 18.7 + 14.3)

= 2 × 33

= 66 cm

According to the question,

The wire is reshaped and bent in the form of a circle.

So,

Perimeter of rectangle = circumference of circle

=> 66 = 66

Therefore,

Circumference of circle = 66 cm

Now,

$\large\Rightarrow{\sf{Circumference=2πr}}$

where,

• r is radius.
• π = 22/7 or 3.14.

$\large\Rightarrow{\sf{66=2\times\dfrac{22}{7}\times\:r}}$

$\large\Rightarrow{\sf{66=\dfrac{44}{7}\times\:r}}$

$\large\Rightarrow{\sf{\dfrac{66\times7}{44}=r}}$

$\large\Rightarrow{\sf{\dfrac{462}{44}=r}}$

$\large\boxed{\sf{r=10.5\:cm.}}$

Now,

Area of circle.

$\large\Rightarrow{\sf{area=π{r}^{2}}}$

$\large\Rightarrow{\sf{area=3.14\times10.5\times10.5}}$

$\large\boxed{\sf{area=346.185\:{cm}^{2}}}$

$\large{\blue{\underline{\boxed{\therefore{\sf{\blue{Radius\:of\:circle\:is\:10.5\:cm.}}}}}}}$

$\large{\blue{\underline{\boxed{\therefore{\sf{\blue{Area\:of\:circle\:is\:346.185\:{cm}^{2}.}}}}}}}$