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tanyasachdeva1

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

  • one year ago
  • one year ago

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

    • one year ago
  2. perl
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    maybe not

    • one year ago
  3. tanyasachdeva1
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    i didnt get it mam

    • one year ago
  4. perl
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    ok , an increase of 72.8% is 172.8% of the original volume. do you agree ?

    • one year ago
  5. perl
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    just like a 100% increase is actually double the original amount (200% of original amount)

    • one year ago
  6. tanyasachdeva1
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    yuppp

    • one year ago
  7. perl
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    ok so New Volume = 1.728 * Old volume

    • one year ago
  8. perl
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    let the old volume be 4/3 pi * r^3. New Volume = 1.728 * 4/3 pi * r^3

    • one year ago
  9. tanyasachdeva1
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    yup but wht abt its surface area ?

    • one year ago
  10. perl
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    we didnt get to that. one step at a time

    • one year ago
  11. perl
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    who is that a picture of?

    • one year ago
  12. tanyasachdeva1
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    ok

    • one year ago
  13. perl
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    so ... New volume = 4/3 pi [(1.728)^(1/3) * r ]^3

    • one year ago
  14. perl
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    see how i brought in the 1.728, by taking the cube root (and then cubing it )

    • one year ago
  15. perl
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    anybody know what a cluster point is ? please help

    • one year ago
  16. tanyasachdeva1
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    ??

    • one year ago
  17. matricked
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    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

    • one year ago
  18. SUROJ
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    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

    • one year ago
  19. tanyasachdeva1
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    thank you so much to all...

    • one year ago
  20. tanyasachdeva1
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    ??

    • one year ago
  21. matricked
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    welcome

    • one year ago
  22. kropot72
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    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 \[\frac{1.44-1}{1}\times 100=44\%\]

    • one year ago
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