Question

On increasing the diameter of a circle by 40%, its area will be increased by

Options

• 40%

•  80%

• 96%

• 82%

Answer 1

 96%
Let d be the original diameter.
Radius `="d"/2`

Thus, we have;

Original area `= π xx ("d"/2)`

`= (pi"a"^2)/4`

New diameter = 140%  of d

`= (140/100xx"d")`

`= (7"d")/5`

Now,

New radius ` =(7"d")/5xx2`

`=(7"d")/10`

New area `= pixx((7"d")/10)^2`

`=(49π"a""^2)/10`

Increase in the area`=((49pi"a"^2)/10 - (pi"a"^2)/4)`` 

`=(24π"a"^2)/100`

`=(6pi"a"^2)/25 `

We have ;

Increase in the area`=((6pi"a"^2)/25xx4/(pi"a"^2)xx100)%`

= 96 %