Question

how to calculate ratio surface atoms to volume for 1 meter gold sphere

Answer 1

1 meter gold sphere means that the diameter of the sphere is 1 meter.

Diameter = 1 m

radius = 0.5 m

surface area of sphere = 4r²

1 meter gold sphere means that the diameter of the sphere is 1 meter. Diameter = 1 m radius = 0.5 m surface area of sphere = 4 pi r^2 volume of sphere = 4/3 pi r^3 ratio of surface area to volume = 4 pi r^2/4/3 pi r^3 = 3/r On solving, we get 3/r. r = 0.5 m So, ratio of surface area to volume = 3/0.5 = 6 m^-1

volume of sphere = 4/3 r³

1 meter gold sphere means that the diameter of the sphere is 1 meter. Diameter = 1 m radius = 0.5 m surface area of sphere = 4 pi r^2 volume of sphere = 4/3 pi r^3 ratio of surface area to volume = 4 pi r^2/4/3 pi r^3 = 3/r On solving, we get 3/r. r = 0.5 m So, ratio of surface area to volume = 3/0.5 = 6 m^-1

ratio of surface area to volume =

$\frac{4\pi r^{2}}{\frac{4}{3}\pi r^{3}} = \frac{3}{r}$

On solving, we get 3/r.

r = 0.5 m

So, ratio of surface area to volume = 3/0.5 = 6 m^-1