Answer

Verified

348.6k+ views

**Hint:**We need to be aware about the formula for perimeter and area of both square and that of a circle. Here, a wire is given in the form of a square i.e. the length of the wire will be its perimeter. Using this information, we could calculate the side of the square. After calculating the side we can use the formula for the circumference of a circle and equate it with the same length and find the radius of the circle. After radius and side have been calculated, the ratio of their areas is easy to calculate.

**Complete step by step answer:**

We are given a wire that has been molded in the shape of a square which means that the perimeter of the square is the length of the wire. The perimeter of a square of side a is $4a$, so we have:

$4a=5024$m

$\implies a=1256$m

Now, the same wire has been converted into a circle. The circumference of a circle of radius $r$ is $2\pi r$, and this will be equal to the length of the wire. So we have:

$2\pi r=5024$m

$\implies \pi r=2512$m

$\implies r=\dfrac{2512}{\pi}$

Now, we need to calculate the ratios of the areas.

Area of the square is given by $a^2$.

Area of a circle is given by $\pi r^2$

So, we need to find:

$\dfrac{{{1256}^{2}}}{\pi \times {{\left( \dfrac{2512}{\pi } \right)}^{2}}}$

$=\dfrac{1256\times 1256\times 22}{2512\times 2512\times 7}$

$=\dfrac{11}{7\times 2}=\dfrac{11}{14}$

Hence, the required ratio is 11:14.

**Note:**If you are not aware about the formulae related to the area and perimeter of a square and circle then you will not be able to solve this question, so it should be known. Moreover, do not try to square such big terms because later on, the ratio is to be found out which means that some terms will automatically get cancelled. So to make least calculation mistakes, do not square the terms prior to finding the ratio.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE