Question

Find the radius (r) of an aluminum cylinder that is 2.60 cm long and has a mass of 13.1 g . For a cylinder, V=πr2l. (The density of aluminum is 2.70 g/cm^3.)

Answer 1

The radius of an aluminum cylinder that is 2.60 cm long and has a mass of 13.1 g, with aluminum having a density of 2.70 g/cm^3, is approximately 0.771 cm.

Step-by-step explanation:

To find the radius (r) of an aluminum cylinder with a length (l) of 2.60 cm and a mass (m) of 13.1 g, given that the density (p) of aluminum is 2.70 g/cm3, we use the formula for the volume of a cylinder, V = πr2l, and the relationship between mass, volume, and density, p = m/V. First, we find the volume of the cylinder using the mass and density:

V = m/p = 13.1 g / 2.70 g/cm3 = 4.852 cm3

Next, we substitute the volume and length into the cylinder volume formula and solve for r:

4.852 cm3 = πr2(2.60 cm)
Rearrange the equation to solve for r2:
r2 = 4.852 cm3 / (π × 2.60 cm)
Find the square root to obtain r:
r ≈ √(4.852 cm3 / (3.14159 × 2.60 cm))
r ≈ √(0.5951 cm) ≈ 0.771 cm

So the radius of the aluminum cylinder is approximately 0.771 cm.

Answer 2

Volume of Aluminium cylinder = mass ÷ density
= 13.1 g ÷ 2.70 g / cm³
= 4.85 cm³

If Volume of Cylinder = πr²l
then 4.85 cm³ = πr²(2.60cm)
thus r² =
`(4.85 cm ^(3) )/( \pi * 2.6 cm)`
∴ r ≈ √(0.594 cm)
≈ 0.771 cm