volume and surface area

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Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The
volume of A is found to be k% lower than the volume of B. The value of k must be
A. 85.5
B. 92.5
C. 90.5
D. 87.5

[amising6]

Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The
volume of A is found to be k% lower than the volume of B. The value of k must be
A. 85.5
B. 92.5
C. 90.5
D. 87.5

formula surafce area =4pir^2
volume 4/3pi r^3
let the radius of sphere A be r1
and radius of sphere B be r2
now given surface area of B is 300% higher than the surface area of A. The
(4ir2^2-4pir1^2)/4pir1^2)*100=300
r2^2-r1^2/ri^2=3
r2^2=4r1^2
r2=+ - 2r1 equation 1(we will take r2=2r1 as r can not be -ve)

volume of A=4/3pi r1^3
volume of B=4/3pi r2^3

4/3pi r2^3=4/3pi r1^3 +(k/100*4/3pi r2^3) (cancelling 4/3 pi both side)
r2^3=r1^3+kr2^3/100 multiplying throughout by 100

100 r2^3=100r1^3+kr2^3
r2^3(100-k)= 100r1^3
(2r1)^3(100 -k)= 100r1^3 (r2=+ - 2r1 equation 1)
8(100-k)=100
700=8k
k=87.5

go step by step

[jeremy8]

Are spheres tested on the GMAT??

I don't remember reading about any sphere formulas anywhere. Just curious, because obviously, if this is on the test I'm in really bad shape right now...

[raunakrajan]

Are spheres tested on the GMAT??

I don't remember reading about any sphere formulas anywhere. Just curious, because obviously, if this is on the test I'm in really bad shape right now...

yea, I have never come across spheres myself!
Rathi could you let us know whats the source of this question?
thanks!
Raunak

[outreach]

it is best to revise all the mensuration formulaes before the exam

Are spheres tested on the GMAT??

I don't remember reading about any sphere formulas anywhere. Just curious, because obviously, if this is on the test I'm in really bad shape right now...

[jeremy8]

it is best to revise all the mensuration formulaes before the exam

Are spheres tested on the GMAT??

I don't remember reading about any sphere formulas anywhere. Just curious, because obviously, if this is on the test I'm in really bad shape right now...

I agree with that, I just don't think these are on the exam at all.