Consider a gold sphere of mass 49 kg. Find its radius.

volumegold= massgold/denstiygold

Volumesphere= 4/3 PI r^3
set them equal, solve for radius r.

To find the radius of the gold sphere, we can use the formula for the volume of a sphere and the information given about its mass.

First, we need to know the density of gold. The density of gold is approximately 19,300 kg/m³. This means that for every cubic meter of gold, it weighs 19,300 kilograms.

To find the volume of the gold sphere, we can use the formula:

Volume = (4/3) * π * radius³

We can rearrange this formula to solve for the radius:

radius = (3 * volume / (4 * π))^(1/3)

Now, let's calculate the volume of the gold sphere. We know that the mass of the sphere is 49 kg. To find the volume, we need to know the density of gold. We can use the formula:

Volume = mass / density

Plugging in the values, we get:

Volume = 49 kg / 19,300 kg/m³

Simplifying this calculation gives us the volume of the gold sphere.

After that, we can substitute the volume into the formula for the radius to obtain the final answer.