Question

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

Answer 1

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

Answer 2

maybe not

Answer 3

i didnt get it mam

Answer 4

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

Answer 5

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

Answer 6

yuppp

Answer 7

ok so New Volume = 1.728 * Old volume

Answer 8

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

Answer 9

yup but wht abt its surface area ?

Answer 10

we didnt get to that. one step at a time

Answer 11

who is that a picture of?

Answer 12

ok

Answer 13

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

Answer 14

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

Answer 15

anybody know what a cluster point is ? please help

Answer 16

??

Answer 17

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

Answer 18

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

Answer 19

thank you so much to all...

Answer 20

??

Answer 21

welcome

Answer 22

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
\[\frac{1.44-1}{1}\times 100=44\%\]