Question

Question #df810

Answer 1

`1/4=25%` of the original area

Explanation:

The area of a circle is given by

`A=pir^2`

where `r` is the radius of the circle.

`A_1=pir_1^2`

`A_2=pir_2^2`

`r_2=1/2r_1`

`:.A_2=pi(1/2r_1)^2=1/4pir_1^2`

`:.A_2=1/4A_1`

So the new area is `1/4=25%` of the original area.

Answer 2

`25%`

Explanation:

`"the area of a circle "=pir^2larrcolor(blue)"original area"`

`"let "r=1/2r`

`rArr"area "=pi(1/2r)^2=1/4pir^2larrcolor(blue)"new area"`

`rArr"new area "/"original area"xx100%`

`=(1/4cancel(pir^2))/cancel(pir^2)xx100%`

`=1/4xx100%=25%`

`"new area is "25%" of the original area"`