What will be increase in area of circle if its radius is increased by 40% - Maths - Circles

Question

What will be increase in area of circle if its radius is
increased by 40%

Harsh Makwana · Accepted Answer

Let the original radius of the circle be r.

Original surface area of circle $n n = n π n n^{n r n n n 2 n n} n n$

New radius = r + 40% of r

$n n = n r n + n \frac{n}{n 40 n} n r n n = n r n n (n \frac{n}{n 140 n} n) n n n = n 1.4 n r n n$

New surface area $n n = n π n n^{n R n n n 2 n n} n = n π n n^{n (n 1.4 n r n) n n n 2 n n} n n$

Now,

Increase in Surface Area $n n = n \frac{n}{n π n n^{n R n n n 2 n n} n - n π n n^{n r n n n 2 n n} n} n n$

$n n = n \frac{n}{n π n n^{n n (n 1.4 n r n) n n n n 2 n n} n - n π n n^{n r n n n 2 n n} n} n n = n \frac{n}{n n^{n n π n (n 1.4 n) n n n n 2 n n} n n^{n r n n n 2 n n} n - n π n n^{n r n n n 2 n n} n} n n = n \frac{n}{n n^{n n (n 1.4 n) n n n n 2 n n} n - n 1 n} n n = n \frac{n}{n 1.96 n - n 1 n} n n = n 1.96 n - n 1 n n = n 0.96 n n = n n 96 n % n n$