Chemistry help plz 2 questions?

Question

1) If the density and circumference of a solid metal ball are known, derive the equation that can be used to find its mass. (Dc^3/6(pi)^2)

2) If the density, mass, and height of a cylinder are known, derive the equation that can be used to find its diameter. (d = 2 square root of m/h(pi)D )

thanks!

Answer 1

This is actually more a Geometry question than Chemistry.

Volume of a spherical ball = (4*Pi*r^3) / 3, r is the radius

Volume of a cyliner = Pi*r^2*L,  r is the radius and L is the length

Density = Mass / Unit Volume so Mass = Density * Volume

Pi = 3.142

Assuming D is the density of both objects:

(1) Mass = (D*4*Pi*r^3) / 3

(2) Mass = D*Pi*r^2*L

Did this make sense? else drop me an email.

=========== here's a more detailed response =========

(Problem 1) Let's first define terms as follows:

Radius of the sphere = R

Circumference of the sphere = C = 2*Pi*R

Volume of the sphere = V = (4/3)*Pi*R^3

Density of the sphere = D

Mass of the sphere = M

C = 2*Pi*R

so R = C/(2*Pi)

so V = (4/3)*Pi*(C/(2*Pi))^3 = (4/3)*Pi*C^3/(8*Pi^3) = C^3/6Pi^2

D = M/V so M = D*V

M = D*C^3/6*Pi^2

Since you know D and C, you can now calculate M

(Problem 2) Again, let's assume some terms

Radius of the cylinder = R

Diameter of the cylinder = 2*R

Length of the cylinder = L

Volume of the cylinder = V = Pi*L*R^2

Density of the cylinder = D

Mass of the cylinder = M

D = M/V or V = M/D

So M/D = Pi*L*R^2

so R^2 = M/(D*L*Pi)

so R = square root (M/(D*L*Pi))

Diameter = 2*R

You know M, D and L so you can calculate Diameter.

Does this clarify things now? Sorry I was a bit vague earlier... and good luck!