Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10kg, what does the sphere weigh

Question

ganeshie8 · Answer

surface are of sphere is proportional to r^2

ganeshie8 · Answer

$\huge r1^2 : r2^2  = 4 : 9$

anonymous · Answer

it says the answer is 33.75 kg but i don't know how to get that

ganeshie8 · Answer

yep.. il walk you through...

anonymous · Answer

okay. Thanks

ganeshie8 · Answer

$\huge r1 : r2  = 2 : 3 $

ganeshie8 · Answer

volume of sphere is proportional to r^3 right ?

anonymous · Answer

i guess

ganeshie8 · Answer

yup it is.. we dont need the actual formula here, as we are dealing with ratios. ..

ganeshie8 · Answer

$\huge r1^3 : r2^3  = 8 : 27$

ganeshie8 · Answer

If the small sphere weighs 10kg, what does the sphere weigh

anonymous · Answer

what does r1^3 and r2^3 mean?

ganeshie8 · Answer

sphere with $r1$ radius weighs $10kg$
we need to find the weight of sphere with $r2$ radius

ganeshie8 · Answer

they are volume ratios. 
since the density is same for both spheres, we can use the volume ratio.

ganeshie8 · Answer

volume of sphere = $\frac{4}{3}\pi r^3$

ganeshie8 · Answer

is it clear ?

anonymous · Answer

i don't really get that

ganeshie8 · Answer

in question, we are given small sphere's weight. and asking us to compute large sphere's weight right ?

anonymous · Answer

yes

ganeshie8 · Answer

1) weight of a sphere is proportional to volume
2) volume of sphere = 4/3 pi r^3
3) so we can take ratio of r^3 to the weight

ganeshie8 · Answer

since they are of same density, weight is proportional to volume. so we can compare volume ratio to weights, right ?

anonymous · Answer

yea

ganeshie8 · Answer

and volume is proportional to r^3

ganeshie8 · Answer

thats how we got to 8:27

ganeshie8 · Answer

we are given surface area ration : 4 : 9

ganeshie8 · Answer

we started from above, right ?

ganeshie8 · Answer

surface area is proportional to r^2

ganeshie8 · Answer

so, ratio of radius must be : 2 : 3
so, ration of volume must be 2^3 : 3^3

anonymous · Answer

okay

ganeshie8 · Answer

8:27 = 10  : x
x = 27*10/8

ganeshie8 · Answer

we are equating volume ratios to weight ratios, because density is same

anonymous · Answer

oh ok

anonymous · Answer

oh I got the answer

ganeshie8 · Answer

below info is needed for this problem :
surface area of sphere = $4\pi r ^2$
volume of sphere = $\frac{4}{3}\pi r^3$

ganeshie8 · Answer

since weight follows volume, we took the volume ratio.

ganeshie8 · Answer

hope it becomes clear later :)...  maybe !!

anonymous · Answer

thank you for your help

ganeshie8 · Answer

u welcome :)