Question

if area of circle is 616 sqcm then find the length of the longest chord of circle​

Answer 1

Answer

$\boxed{\textbf{\large{28cm}}}$

Explanation

☑ The longest chord of a circle is a diameter of a circle

so, we have given,

Area of a circle = 616 sqcm

☑ The formula to find the Area of a circle is

☑ Area of circle = π (r )^2

☑ [value of π is 22/7 or 3.14]

616 = 22/7 (r) ^2

[616 X 7]/ 22 = (r) ^2

[4312]/22 = (r) ^2

√196 = r

r = 14 [r is a radius ]

☑ diameter = 2r

= 14 X 2

= 28

therefor the length of the longest chord of a circle is

$\boxed{\textbf{\large{28cm}}}$

Answer 2

Solution :-

As provided :-

Area of the circle = 616 cm²

And question asks about the longest chord of the circle .

First of all we should know these things :-

▪️What is a chord ?

» A chord is line joining the two points on the circumference of the circle.

▪️Which one is the longest chord ?

» We know that out of every line joining the two points on the circumference of the circle diameter is the longest one which divides the circle into two equal parts.

So longest chord = Diameter of the circle.

▪️Area of a circle = πr²

Where r = radius of the circle.

Now as given

Area of the circle = 616 cm²

$\rightarrow \pi r^2 = 616$

$\rightarrow r^2 = \dfrac{616}{\pi}$

$\rightarrow r^2 = \dfrac{616}{\dfrac{22}{7}}$

$\rightarrow r^2 = \dfrac{616}{22} \times 7$

$\rightarrow r^2 = 28 \times 7$

$\rightarrow r^2 = 196$

$\rightarrow r = \sqrt{196}$

$\rightarrow r = \pm 14$

Now as length cannot be negative

$r = 14 \: cm$

Now as diameter = 2 × radius

$\large{\boxed{\sf{ Diameter = 28 \: cm }}}$