How does the volume of particle Y compare to particle X if Y has a diameter of 300 micrometers and X has a diameter of 150 micrometers?

To determine how the volume of particle Y compares to particle X, we start by using the formula for the volume of a sphere, as particles are often approximated as spheres in these calculations. The volume ( V ) of a sphere is calculated using the formula:

[ V = \frac{4}{3} \pi r^3 ]

where ( r ) is the radius of the sphere.

First, we need to find the radii of both particles from their diameters:

• For particle Y, the diameter is 300 micrometers, so the radius ( r_Y ) is 150 micrometers.

• For particle X, the diameter is 150 micrometers, so the radius ( r_X ) is 75 micrometers.

Next, we can compute the volumes:

• Volume of particle Y:

[ V_Y = \frac{4}{3} \pi (r_Y)^3 = \frac{4}{3} \pi (150)^3 ]

• Volume of particle X:

[ V_X = \frac{4}{3} \pi (r_X)^3 = \frac{4}{3} \pi (75)^3 ]

Now, to compare the