Question

A wire in the form of a rectangle 57cm and 35cm is reshaped in the form of a circle. Find the radius and the area of the circle.

Answer 1

as the same wire is used perimeter of rectangle=perimeter of circle
perimeter of rectangle=2(l+b)=2(57+35)=2×92=184
perimeter of circle=184
so 2$\pi$ r=184
2×$\frac{22}{7}$×r=184

so r=$\frac{184*7}{2*22}$

so r=$\frac{322}{11}$ cm

area=$\pi$r²

=$\frac{22}{7}* \frac{322}{11} *\frac{322}{11}$

=$\frac{29624}{11}$ cm²

Answer 2

Answer:

Since the wire is reshaped into a circle, the total length of the wire would remain the same. Hence we can say that the perimeter of the wire in rectangular form would the same as that in the circular form.

Hence Perimeter of rectangular form is given as:

→ 2 ( l + b )

→ 2 ( 57 + 35 )

→ 2 ( 92 ) = 184 cm

Hence the circumference of the circular wire is also 184 cm.

→ 2πr = 184 cm

→ r = 184 / 2π

→ r = 184 / 6.28

→ r = 29.3 cm ( approx )

Hence the area of wire in circular form is given as:

→ Area = πr²

→ Area = 3.14 × 29.3 × 29.3

→ Area = 2695.65 cm² ( approx. )