## tanyasachdeva1 2 years ago if volume of sphere increases by 72.8% what happen to the surface area?

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1. perl

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

2. perl

maybe not

3. tanyasachdeva1

i didnt get it mam

4. perl

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

5. perl

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

6. tanyasachdeva1

yuppp

7. perl

ok so New Volume = 1.728 * Old volume

8. perl

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

9. tanyasachdeva1

yup but wht abt its surface area ?

10. perl

we didnt get to that. one step at a time

11. perl

who is that a picture of?

12. tanyasachdeva1

ok

13. perl

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

14. perl

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

15. perl

16. tanyasachdeva1

??

17. matricked

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

18. SUROJ

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

19. tanyasachdeva1

thank you so much to all...

20. tanyasachdeva1

??

21. matricked

welcome

22. 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 $\frac{1.44-1}{1}\times 100=44\%$