Diameter of a sphere is deereased by 25%o. What
is the deerease in percent in surface area of sphere.
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Answer:
Step-by-step explanation:
ANSWER
Original Diameter ==d
Original CSA=4\pi\left(\dfrac{d}{2}\right)^2=\pi d^2=4π(
2
d
)
2
=πd
2
New Diameter =d-\dfrac{25}{100}d=\dfrac{3d}{4}=d−
100
25
d=
4
3d
New CSA=4\pi \left(\dfrac{3d}{8}\right)^2=\dfrac{9}{16}\pi d^2=4π(
8
3d
)
2
=
16
9
πd
2
.
\%% decrease =\dfrac{(\pi d^2-\dfrac{9}{16}\pi d^2)}{\pi d^2}\times 100=
πd
2
(πd
2
−
16
9
πd
2
)
×100
=\dfrac{\pi d^2}{\pi d^2}\left(1-\dfrac{9}{16}\right)\times 100=
πd
2
πd
2
(1−
16
9
)×100
=\dfrac{16-9}{16}\times 100=
16
16−9
×100
=43.75\%=43.75%
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