A styrofoam sphere of radius R has a density ρ.You now carefully compress the sphere so its radius is R/2.What is the density of the compressed sphere?

Question

Quizplus · Accepted Answer

The density of an object is given by its mass divided by its volume. When the radius of the sphere is halved, its volume decreases by a factor of $ \left(\frac{1}{2}\right)^3 = \frac{1}{8} $. Since the mass remains constant but the volume decreases to 1/8th of its original volume, the density increases by a factor of 8, making the new density $8 \rho$.

A Styrofoam Sphere of Radius R Has a Density ρ 8\sqrt { 8 }8​

A Styrofoam Sphere of Radius R Has a Density ρ $\sqrt { 8 }$