Question

The diameter of a sphere is decreased by 20%.By what percent does its C. S. A decrease Plz solve this question

Answer 1

let,
diameter of sphere=x
decreased %in diameter=20%
therefore,
decreased %of diameter=20% of x
=20/100xX
=1/5x
now,
decreased diameter=x-1/5x
=5x-1x/5
=4x/5
when,
diameter=x
radius=x/2
therefore,
csa of sphere=4πr^2
=4πxX/2xX/2
=4πxX^2/4
=πx^2
when,
diameter=4x/5
radius=4x/5/2
=4x/10
Now,
csa=4πr^2
=4πx(4x/10)
=4πx 16x^2/100=16x^2/25
therefore, decreased csa=πx^2-16x^2/25
=πx^2(1-16)/25
=πx^2(25-16)/25
=πx^2x9/25
in %=πx^2x9/25/πx^2 x100%
=9/25/100
=36%