Final answer:
The mass of an aluminum ball with a radius of 1 cm and a density of 2.7 g/cm³ is calculated to be approximately 11.31 grams, using the volume formula for a sphere and the definition of density.
Step-by-step explanation:
To calculate the mass of an aluminum ball with a radius of 1 cm and a density of 2.7 g/cm³, we use the formula for the volume of a sphere (V = ¾πr³) and the definition of density (ρ = m/V).
The volume (V) of the ball is:
V = ¾π(1 cm)³ = ¾π(1 cm)³
V = ¾(3.14)(1 cm)³ = ¾(3.14)(1 cm³)
V = ¾(3.14) = 4.19 cm³ (approximately)
Now, we use the density to find the mass (m):
m = ρ × V = 2.7 g/cm³ × 4.19 cm³
m = 11.31 g (approximately)
The mass of the aluminum ball can be calculated using the formula:
Mass = Density x Volume
The volume of a sphere can be calculated using the formula:
Volume = (4/3) x π x radius^3
Substituting the given values, we have:
Mass = Density x ((4/3) x π x radius^3)
Mass = 2.7 g/cm³ x ((4/3) x 3.14 x (1 cm)^3)
Mass = 2.7 g/cm³ x (4.18 cm³)
Mass = 11.31 g