Find the percentage decrease in the csa of a sphere , if it's diameter is decreased by 25%
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Answered by
3
let original diameter be d that is 2r
new diameter=3/4d or 3/2r
original CSA 4*pi*r^2
=4*pi*4r^2=16*pi*r^2
new CSA=4*pi*9/4r^2
=9*pi*r^2
decrease=7*pi*r^2
decrease℅=(7*pi*r^2/16*pi*r^2)*100
=43.75℅
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Answered by
6
let original diameter be 2x
then radius =x
c.s.a=4×pi×r^2
decreased diameter of sphere=2x-25% of 2x
=2×-x/2=3/2x
decreased radius=3/4x
so,decreased c.s.a=
4×pi(3/4x)^2
=9/4×pi×x^2
decrease in area=
4×pi×x^2-9/4×pi×x^2
=7/4×pi×x^2
so, decreased percentage in c.s.a=7/4×pi×x^2/4×pi×x^2×100%=7/16×100%=43.75%
then radius =x
c.s.a=4×pi×r^2
decreased diameter of sphere=2x-25% of 2x
=2×-x/2=3/2x
decreased radius=3/4x
so,decreased c.s.a=
4×pi(3/4x)^2
=9/4×pi×x^2
decrease in area=
4×pi×x^2-9/4×pi×x^2
=7/4×pi×x^2
so, decreased percentage in c.s.a=7/4×pi×x^2/4×pi×x^2×100%=7/16×100%=43.75%
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