Question

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?

Answer 1

w= 33.75, the weight of the larger sphere

Answer 2

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