Question

if sum of the radius and circumference of a circle is 51 then find the area

Answer 1

Let the radius = r

It's circumference = 2πr

Now,

According to the question :

r+2πr = 51

r(1+2×22/7)= 51

$r ( 1 + 2 \times { \frac{22}{7} } ) = 51\\ r(1 + \frac{44}{7} ) = 51 \\ r( \frac{7 + 44}{7} ) = 51\\ r( \frac{51}{7} ) = 51 \\ r = 51 \times \frac{7}{51} \\ r = 7 \: units$

Then, Area of the circle = πr² =

$\frac{22}{7} \times {7}^{2} \\ \frac{22}{7} \times 7 \times 7 \\ 22 \times 7 \\ = 154$

Answer = The required area is = 154 units ².