A styrofoam sphere of radius R has a density $\rho .$ You now carefully compress the sphere so its radius is R/2 . What is the density of the compressed sphere?
A) $8 \rho$
B) $4 \rho$
C) $\rho \sqrt { 2 }$
D) $\rho \sqrt { 8 }$
E) $2 \rho$

Question

A styrofoam sphere of radius  R  has a density $\rho .$ You now carefully compress the sphere so its radius is  R/2 . What is the density of the compressed sphere?
A) $8 \rho$
B) $4 \rho$
C) $\rho \sqrt { 2 }$
D) $\rho \sqrt { 8 }$
E) $2 \rho$

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 $2^3 = 8$ (since volume $V = \frac{4}{3}\pi r^3$). The mass remains constant, so the density increases by a factor of 8 to compensate for the decrease in volume, making the new density $8 \rho$.

A Styrofoam Sphere of Radius R Has a Density