Question #df810

2 Answers
Nam D.
Jan 5, 2018

#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.

Jim G.
Jan 5, 2018

#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"#

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