Final answer:
To find the radius of a solid aluminum sphere with a mass of 80 g, we use the density of aluminum (2.70 g/cm³) to calculate the volume and then find the radius. Converting centimeters to inches, we find the radius is approximately 0.701 inches.
Step-by-step explanation:
To find the radius of a solid aluminum sphere using its mass, we apply the formula for the volume of a sphere and the concept of density. The density of aluminum is 2.70 g/cm³. We are given that the mass (m) of the aluminum sphere is 80 g.
The formula for the density is ρ = m / V, where ρ is density, V is volume, and m is mass. We can rearrange this formula to solve for V, the volume of the sphere: V = m / ρ. Once we have the volume, we can find the radius using the volume formula for a sphere, V = 4/3 π r³.
Step-by-Step Calculation
- Calculate the volume of the sphere: V = 80 g / 2.70 g/cm³ = 29.63 cm³.
- Calculate the radius of the sphere. Starting from V = 4/3 π r³, solve for r: r³ = V / (4/3 π) = 29.63 cm³ / (4/3 π). Therefore, r ≈ 1.781 cm.
- Finally, to convert the radius from centimeters to inches we use the conversion factor 1 inch = 2.54 cm: radius in inches = 1.781 cm / 2.54 cm/inch ≈ 0.701 inches.