Question

the ratio of circumference and area of a circle is 2:7 find its circumference

Answer 1

let,
the circumference be 2x
the area of circle be 7x
given,
the ratio of circumference and area of circle = 2:7

$2\pi \times r \div \pi \times r \times r= 2x \div 7x$
$2 \div r = 2 \div 7$
$r = 2 \times 7 \div 2$
$r = 7cm$
$circumfernce = 2\pi \times r$
=2*22/7*7
=44cm

Answer 2

Question :-

The ratio of circumference and area of a circle is 2:7 find its circumference.

Given :

The ratio of circumference and area of a circle is 2:7 .

To find :

What is the Circumference of circle ?

Solution :

✦ Circumference of Circle = 2πr

✦ Area of circle = πr²

Now , as per the Question :-

By applying the above formula, we get

$\longrightarrow\sf 2\pi r : \pi r^2 = 2 : 7 \\\\\\ \longrightarrow\sf \dfrac{2 \pi r}{\pi r^2} = \dfrac{2}{7} \\\\\\ \longrightarrow\sf \dfrac{2}{r} = \dfrac{2}{7} \\\\\\ \longrightarrow\bold{2r = 14} \dots \dots (i)$

Circumference of circle,

$\longrightarrow\sf Circumference_{circle} = 2 \pi r \\\\\\ \longrightarrow\sf Circumference_{circle} = 2r \times \pi \\\\\\ \longrightarrow\sf Circumference_{circle} = 14 \times \pi \\\\\\ \longrightarrow\underline{\boxed{\bold{Circumference_{circle} = 14 \pi }}} \\\\\\\\ \underline{\sf{C \ = 14 \pi \ units \ \ [Circumference \: of \: circle] }}$

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .