Question

A uniform lead sphere and a uniform aluminum sphere have the same mass. What is the ratio of the radius of the aluminum sphere to the radius of the lead sphere? (Density of Al: 2.7x10^3 kg/m³, Density of Pb: 11.3x10^3 kg/m³)

A) 2:1
B) 1:2
C) 1:4
D) 4:1

Answer 1

The ratio of the radius of the aluminum sphere to the radius of the lead sphere is approximately 1:2.

Step-by-step explanation:

To find the ratio of the radius of the aluminum sphere to the radius of the lead sphere, we need to use the formula for the density of a sphere:

Density = Mass / Volume

Since the spheres have the same mass, they will also have the same volume. Therefore, the ratio of their radii will be the square root of the ratio of their densities, because the volume of a sphere is proportional to the cube of its radius:

Ratio of radii = √(Density of aluminum / Density of lead)

Substituting the given densities of aluminum and lead, we get:

Ratio of radii = √(2.7x10^3 kg/m³ / 11.3x10^3 kg/m³)

Simplifying this expression gives us a ratio of approximately 0.51. Therefore, the ratio of the radius of the aluminum sphere to the radius of the lead sphere is approximately 1:2.