Find the volume of a sphere if its surface has an area of 615.44 dm2.

The surface area of the ball is S = 4 * pi * R², therefore, from the known value of the surface area, you can find the radius of this ball by the formula:

R = √ (S / 4 / pi).

For a sphere with a surface area equal to 615.44 dm², the radius is:

R = √ (615.44 / 4 / 3.14) = √ (153.86 / 3.14) = √49 = 7 dm.

The volume of the ball is V = 4/3 * pi * R³, therefore, the volume of the ball with a radius of 7 dm is equal to:

V = 4/3 * 3.14 * 7³ = 4/3 * 3.14 * 343 = 4308.08 / 3 ≈ 1436.03 dm³.

Answer: the volume of the ball is 1436.03 dm³.