We'll calculate the volume exactly how the shape is formed: finding a cube and cutting a piece of it out. First, we can find the volume of the whole cube (whole, not holed), and then we can subtract the volume of the cylinder. For a cube, the length, width, and height are all the same. V_{cube} = s^{3} = (10 cm)^{3} = 1000 cm^{3} Now we surgically remove the cylinder. Its diameter is 5 cm, meaning the radius is 2.5 cm. The height of the cylinder is the same as the edge of the cube: 10 cm. V_{cylinder} = πr^{2}h V_{cylinder} = π(2.5 cm)^{2}(10 cm) V_{cylinder} = 62.5π ≈ 196.3 cm^{3} That means our final volume is the cube minus the cylinder. V_{total} = V_{cube} – V_{cylinder} V_{total} = 1000 cm^{3} – 196.3 cm^{3} V_{total} = 803.7 cm^{3} |