first you must find the equations for the surface area and for the volume of a sphere.
I believe the volume is 4/3 *pi *r^3,
making the surface area 4*pi*r^2
the ratio is the one number over the other so:
(4*pi*r^2)/(4/3*pi*r^3) = 3/r
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0.6 is the surface area to volume ratio.
Surface area to volume ratio in nanoparticles have a significant effect on the nanoparticles properties. Firstly, nanoparticles have a relative larger surface area when compared to the same volume of the material. For example, let us consider a sphere of radius r: The surface area of the sphere will be 4πr2 The volume of the sphere = 4/3(πr3) Therefore the surface area to the volume ratio will be 4πr2/{4/3(πr3)} = 3/r It means that the surface area to volume ration increases with the decrease in radius of the sphere and vice versa.
Well, first of all, that's no sphere.-- A sphere with surface area = 300 has volume = 488.6.-- A sphere needs surface area of 304.6 in order to have volume = 500.But this is just a ratio exercise, not a geometry problem, so we'll just use the numbersgiven in the question. It's just some sort of wacky humongous paramecium:Surface area = 300Volume = 500Ratio of (surface area)/(volume) = 300/500 = 0.6 .
3 to 7
This is pretty easy, just divide 432 by 864 and you get a 1:2 ratio.