The density of the metal is 0.291 g/cm³. The cube weighed 0.356 N before the hole was drilled in it.
(a) What is the density of this metal?
The volume of the cube can be calculated by using the formula: volume = side^3. In this case, the side length is 5.0 cm, so the volume is (5.0 cm)^3 = 125.0 cm³. Since the hole drilled through the cube is a cylinder, its volume can be calculated using the formula for the volume of a cylinder: volume = π * radius^2 * height. In this case, the radius is half the diameter, so the radius is 2.0 cm / 2 = 1.0 cm. The height of the cube is the side length, so the height is 5.0 cm. The formula for density is density = mass / volume. Given that the cube weighs 7.50 N = 7.50 kg (since weight is the force due to gravity and the acceleration due to gravity is approximately 9.8 m/s²), we can calculate the density as (7.50 kg) / (125.0 cm³ - π * (1.0 cm)^2 * 5.0 cm) = 0.291 g/cm³.
(b) What did the cube weigh before you drilled the hole in it?
The weight of the cube before drilling the hole can be calculated based on the density and the volume of the cube. Using the formula for weight, weight = mass * acceleration due to gravity, we can rearrange the formula for density to solve for mass: mass = density * volume. Given the density of 0.291 g/cm³ and the volume of the cube as 125.0 cm³, the mass of the cube is (0.291 g/cm³) * (125.0 cm³) = 36.375 g. Converting the mass to a weight, we have weight = mass * acceleration due to gravity = (36.375 g) * (9.8 m/s²) = 0.356 N.