We can see that the total volume of material that makes up the ball is approximately 7,544.75 cm³.
To find the total volume of material that makes up the ball, we need to subtract the volume of the inner hollow part from the volume of the outer sphere.
The outer diameter of the ball is given as 50 cm. Since the diameter is twice the radius, the radius of the outer sphere is 50 cm / 2 = 25 cm.
The formula for the volume of a sphere is V = (4/3) × π × r³, where r is the radius.
Substituting the value of the radius, we get V_outer = (4/3) × π × (25 cm)³.
The thickness of the material that makes up the ball is given as 1 cm. Therefore, the inner radius is the outer radius minus the thickness: r_inner = 25 cm - 1 cm = 24 cm.
Using the same formula, we can calculate the volume of the inner hollow part: V_inner = (4/3) × π × (24 cm)³.
To find the total volume of material, we subtract the volume of the inner hollow part from the volume of the outer sphere: V_material = V_outer - V_inner.
Now, let's calculate the values:
V_outer = (4/3) × π × (25 cm)³ ≈ 65,449.85 cm³
V_inner = (4/3) × π × (24 cm)³ ≈ 57,905.09 cm³
Finally, we subtract V_inner from V_outer to find the total volume of material:
V_material ≈ V_outer - V_inner ≈ 65,449.85 cm³ - 57,905.09 cm³ ≈ 7,544.75 cm³. (rounded to the nearest hundredth)
Therefore, the total volume of material that makes up the ball is approximately 7,544.75 cm³.