Question

If a copper wire is bend to make a square whose area is 729 cm2. If the same wire is bent to form a semicircle, then find the radius of semicircle?

Answer 1

Answer:

The radius of the semicircle is 15.237 cm

Step-by-step explanation:

Let the side of the square be 'a' cm

It is given that area of the square is 729 cm^2

Therefore

${a}^{2} = 729 \\ a = \sqrt{729 } \\ a = 27$

Now,

Since the same wire is bent to form a circle ,

The area remains the same.

Therefore,

area of a semi circle,

$\pi {r}^{2} \div 2$

Since the area remains same

Therefore

${a}^{2} = \pi {r}^{2} \\ 729 = 3.14 \times {r}^{2} \\ {r}^{2} = 729 \div 3.14 \\ {r}^{2} = 232.17 \\ r = \sqrt{232.17} \\ r = 15.237$