One cubic meter of granite has a mass of 2.70E3 kg, and one cubic meter of gold has a mass of 1.93E4 kg. Find the radius of a granite sphere whose mass is the same as that of a gold sphere of radius 1.07 cm.

Any help is appreciated!!

To find the radius of the granite sphere, we need to compare its mass to the mass of the gold sphere.

Let's start by finding the mass of the gold sphere. The density of an object is defined as its mass divided by its volume. We can find the volume of the gold sphere using the formula for the volume of a sphere: V = (4/3) * π * r^3, where r is the radius.

Given that the mass of the gold sphere is 1.93E4 kg and the radius is 1.07 cm, we can set up the following equation:

1.93E4 kg = (4/3) * π * (1.07 cm)^3 * density of gold

Next, we need to find the density of gold. The density of gold is given as the mass of one cubic meter of gold divided by the volume of one cubic meter. We are told that the mass of one cubic meter of gold is 1.93E4 kg, so the density of gold is:

density of gold = 1.93E4 kg / 1 m^3

Now we can substitute this value into our earlier equation:

1.93E4 kg = (4/3) * π * (1.07 cm)^3 * (1.93E4 kg / 1 m^3)

To find the radius of the granite sphere, we will use the same equation:

mass of granite sphere = (4/3) * π * r^3 * density of granite

We are given the mass of the granite sphere (2.70E3 kg), and we need to solve for the radius, so we can set up the equation as follows:

2.70E3 kg = (4/3) * π * r^3 * density of granite

Now we can equate the two equations:

(4/3) * π * (1.07 cm)^3 * (1.93E4 kg / 1 m^3) = (4/3) * π * r^3 * density of granite

The density of granite is not given, but we can assume that it is the same for both the granite and gold spheres. Therefore, we can cancel out the density terms:

(1.07 cm)^3 * (1.93E4 kg / 1 m^3) = r^3

Now we can solve for r by finding the cube root of both sides:

r = (1.07 cm)^3 * (1.93E4 kg / 1 m^3)^(1/3)

Calculating this expression will give us the radius of the granite sphere whose mass is the same as that of the gold sphere.

The masses are the same?

mass=density*volume

densitygold*PI*4/3*1.07^3 = densityrock*PI*4/3*x^3

solve for x. I will be happy to critique your work.