if volume of sphere increases by 72.8% what happen to the surface area?

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- anonymous

if volume of sphere increases by 72.8% what happen to the surface area?

- katieb

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- perl

V = 4/3 pi r^3 . this is a calculus differential question>

- perl

maybe not

- anonymous

i didnt get it mam

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- perl

ok , an increase of 72.8% is 172.8% of the original volume. do you agree ?

- perl

just like a 100% increase is actually double the original amount (200% of original amount)

- anonymous

yuppp

- perl

ok so New Volume = 1.728 * Old volume

- perl

let the old volume be 4/3 pi * r^3.
New Volume = 1.728 * 4/3 pi * r^3

- anonymous

yup but wht abt its surface area ?

- perl

we didnt get to that. one step at a time

- perl

who is that a picture of?

- anonymous

ok

- perl

so ...
New volume = 4/3 pi [(1.728)^(1/3) * r ]^3

- perl

see how i brought in the 1.728, by taking the cube root (and then cubing it )

- perl

anybody know what a cluster point is ? please help

- anonymous

??

- anonymous

since volume is directly proportional to r^3
hence if new volume is (100%+72.8%)=1.728 times the old volume
then new r =cube root of (1.728) times old radius
hence new r=1.2 times old r
as surface area is directly proportional to r^2
hence new surface area =(1.2)^2 times old surface area=1.44 times old surface area
hence increase in surface area =.44 times=44% increase

- anonymous

Volume and surface area both depends on radius........so, you need to understand and calculate what happens to radius when volume increase by that much

- anonymous

thank you so much to all...

- anonymous

??

- anonymous

welcome

- kropot72

The volume of a sphere is proportional to the radius cubed:
\[volume=\frac{4}{3}\pi r ^{3}\]
The surface area of a sphere is proportional to the radius squared:
\[Surface\ area=4\pi r ^{2}\]
Let the original radius = 1 unit
Then for the volume to increase by 72.8%, the cube of the radius must increase from 1unit cubed up to 1.728 units cubed. This means the radius has increased from 1 unit up to \[\sqrt[3]{1.726}=1.2\ units\]
Since the surface area is proportional to the radius squared, the square of the radius will increase from 1 unit squared up to
\[1.2^{2}=1.44\]
Therefore the surface area has increased by
\[\frac{1.44-1}{1}\times 100=44\%\]

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