The mass of an object can be calculated using the formula:
Mass = Density × Volume
In this case, we need to find the mass of a solid cube of aluminum. Given:
- Density of aluminum = 2700 kg/m3
- Edge length of the cube = 1.5 cm
First, we need to calculate the volume of the cube. The volume V of a cube with edge length a is given by:
V = a3
Substitute the edge length:
V = (1.5 cm)3 = 1.5 × 1.5 × 1.5 cm3 = 3.375 cm3
Since the density is given in kg/m3, we should convert the volume from cm3 to m3. There are 1,000,000 cm3 in 1 m3, so:
Volume in m3 = 3.375 cm3 × (1 m3/1,000,000 cm3) = 3.375 × 10-6 m3
Now, use the mass formula:
Mass = Density × Volume
Mass = 2700 kg/m3 × 3.375 × 10-6 m3
This equals:
Mass = 9.1125 × 10-3 kg
Convert kg to grams (since 1 kg = 1000 g):
Mass = 9.1125 grams
So, the mass of the cube is approximately 9.1 g. Thus, the correct answer is 9.1 g.