volume and surface area

[email protected] wrote: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

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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 wrote: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

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

jeremy8 wrote: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...

outreach wrote:it is best to revise all the mensuration formulaes before the exam

jeremy8 wrote: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.