Question

A wire of length 210cm is the first bent into a square and then into a circle. Which one have nore area. Explain​

Answer 1

Step-by-step explanation:

The length of the wire is 210cm. So definitely the perimeter of square which is made is also 210 cm. So from perimeter of square we can find length of each side of a square.

$perimeter = 4l \\ 210 = 4l \\ l = 210 \div 4 = 52.5$

As we have length of each side now we can find area of square,

$area \: of \: square= {l}^{2} \\ area \: of \: square = (52.5)^{2} \\ area \: of \: square = 2756.25 {cm}^{2}$

Similarly,

As the length of the wire is 210cm, the perimeter of circle will also be 210cm. So what we do is, first find radius using perimeter then put radius in area formula and get area of circle.

$perimeter = 2\pi \: r \\ 210 = 2\pi \: r \\ r = 210 \div 2\pi \\ r = 33.41 \: where \: \pi = 3.14$

Now putting value of r in area formula of circle,

$area \: of \: circle \: = {\pi \: r}^{2} \\ area \: of \: circle = 3.14 \times (33.41) ^{2} \\ area \: of \: circle = 3504.96 {cm}^{2}$

Here area of circle>area of square.

So, area of circle is more.

Thankyou

Answer 2

Correct Question:-

A wire of length 210cm is the first bent into a square and then into a circle. Which one have greater area?

Answer:-

★ Given:

• Length of wire = 210 cm

• Wire bent into square

• Wire bent into circle

★ To Find:

• Which one have greater area Square or Circle?

★ Solution:

➥ Finding side of square.

According to given conditions

Perimeter of square = length of wire

➠ 4 × Side = 210cm

➠ Side = 210 ÷ 4

➠Side = 52.5cm

➥ Finding Area of square

Area of square = Side × Side

= 52.5 × 52.5

= 2756.25cm²

➥ Finding radius of circle

According to given conditions

Circumference of circle = length of wire

➠ 2πr = 210cm

➠ πr = 210 ÷ 2

➠ r = 105 ÷(22/7)

➠ r = (105 × 7) ÷ 22

➠ r = 33.42(approx.)

➥ Finding area of circle

Area of circle = πr²

= π × 33.42²

= 3508.83cm²

As,

3508.83cm² is greater than 2756.25cm²

Hence, Area of circle is greater than area of square.

Formula to be remembered:-

▪︎Perimeter of rectangle = 2(l+b)

▪︎Perimeter of square = 4 × Side

▪︎Circumference of circle = 2πr

▪︎Perimeter of triangle = Sum of all sides

▪︎Area of rectangle = length × breadth

▪︎Area of square = Side × Side

▪︎Area of circle = πr²

▪︎Area of triangle = ½ × Base × Height

or

by Heron's Formula