Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the large sphere weigh?

We know the surface areas:

Sphere Surface Area = 4 • π • r²

radius^2 = Surface Area / 4 * PI

Let's say area of smaller sphere is 4 PI

radius^2 = 1

radius = 1

9/4 = 2.25

Area of the larger sphere = 4 * PI * 2.25

radius^2 = 2.25

radius = 1.5

Volume of a sphere = 4/3 • π • r³

Volume of larger sphere = 4/3 • π • 1.5^3

Volume of larger sphere = 3.375 times volume of smaller sphere

Mass of larger sphere = 3.375 * 10 kg

The larger sphere weighs 33.75 kg

w = 33.75, the weight of the larger sphere