The earth is approximately a sphere of average diameter 12740km.

The smallest of the planets is Mercury, also spherical, with average diameter 4840km. Determine what percentages (to the nearest hundredth) the volume and surface area of Mercury are of those of the Earth.

area ratio = Dm^2/De^2

volume ratio = Dm^3/De^3

To determine the percentages of the volume and surface area of Mercury in comparison to Earth, we need to calculate the volume and surface area of both planets.

Let's start with calculating the volume:

The volume of a sphere can be calculated using the formula: V = (4/3) * π * r^3
Where V is the volume and r is the radius of the sphere.

For Earth:
Radius (r) = diameter / 2 = 12,740 km / 2 = 6,370 km
V(Earth) = (4/3) * π * (6,370 km)^3

For Mercury:
Radius (r) = diameter / 2 = 4,840 km / 2 = 2,420 km
V(Mercury) = (4/3) * π * (2,420 km)^3

Now, let's calculate the surface area:

The surface area of a sphere can be calculated using the formula: A = 4 * π * r^2
Where A is the surface area.

For Earth:
A(Earth) = 4 * π * (6,370 km)^2

For Mercury:
A(Mercury) = 4 * π * (2,420 km)^2

Finally, we can calculate the percentages:

Percentage volume of Mercury = ( V(Mercury) / V(Earth) ) * 100
Percentage surface area of Mercury = ( A(Mercury) / A(Earth) ) * 100

Plugging in the values and calculating these percentages will give us the desired results.