Question

if diameter of a circle is increased by 40% then the area increased by how much

Answer 1

let the initial diameter of the circle be
$d$
so, ATQ, it increased by 40%, so, new diameter is
$d + \frac{40d}{100}$
or, new diameter is.
$d \frac{140}{100}$
now, initial area of circle is
$\pi \times d$
so new area is
$\pi \: d \: \frac{140}{100}$
and so the increase in area is
$\pi \times d( \frac{140 - 100}{100} )$
which implies
$\pi \: d( \frac{40}{100} )$
and since π•d was the original area, so the area also increased by 40%