anonymous
  • anonymous
if volume of sphere increases by 72.8% what happen to the surface area?
Mathematics
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anonymous
  • anonymous
if volume of sphere increases by 72.8% what happen to the surface area?
Mathematics
katieb
  • katieb
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perl
  • perl
V = 4/3 pi r^3 . this is a calculus differential question>
perl
  • perl
maybe not
anonymous
  • anonymous
i didnt get it mam

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perl
  • perl
ok , an increase of 72.8% is 172.8% of the original volume. do you agree ?
perl
  • perl
just like a 100% increase is actually double the original amount (200% of original amount)
anonymous
  • anonymous
yuppp
perl
  • perl
ok so New Volume = 1.728 * Old volume
perl
  • perl
let the old volume be 4/3 pi * r^3. New Volume = 1.728 * 4/3 pi * r^3
anonymous
  • anonymous
yup but wht abt its surface area ?
perl
  • perl
we didnt get to that. one step at a time
perl
  • perl
who is that a picture of?
anonymous
  • anonymous
ok
perl
  • perl
so ... New volume = 4/3 pi [(1.728)^(1/3) * r ]^3
perl
  • perl
see how i brought in the 1.728, by taking the cube root (and then cubing it )
perl
  • perl
anybody know what a cluster point is ? please help
anonymous
  • anonymous
??
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
  • 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
  • anonymous
thank you so much to all...
anonymous
  • anonymous
??
anonymous
  • anonymous
welcome
kropot72
  • 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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