A hollow metal ball has an external radius of 6 cm and an internal radius of 3 cm. What is the volume of metal in the ball, in cubic cm? (Leave the answer in terms of π.)

The metal is the outer sphere minus the hollow, so its volume = (4/3)π$(R^3-r^3)=(4/3)$π$(216-27)=(4/3)$π $x$ 189 = 252π cubic cm. The trap 189π drops the 4/3 from the sphere's formula; 288π = (4/3)π $x$ 216 is the solid ball of radius 6 with the cavity never removed; 36π = (4/3)π$(6-3{)}^3$ subtracts the radii FIRST and then cubes, but $R^3-r^3=189$ is nothing like $(R-r{)}^3=27$.