Question

Find the radius of an aluminum cylinder that is 2.00 cm long and has a mass of 12.4 g.

Answer 1

To find the radius of the aluminum cylinder, divide the volume by the height and solve for r using the formula for the volume of a cylinder.

Step-by-step explanation:

To find the radius of an aluminum cylinder, we need to use the formula for the volume of a cylinder, which is given by V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, the length (height) of the cylinder is given as 2.00 cm. We can calculate the volume using the mass of the cylinder and the density of aluminum, which is approximately 2.70 g/cm³.

Using the formula for density, which is given by density = mass/volume, we can rearrange the formula to solve for the volume. We have the mass of the cylinder as 12.4 g, so plugging in the values, we get:

12.4 g = (2.70 g/cm³) * V

Solving for V, we find that V = 12.4 g / (2.70 g/cm³) ≈ 4.59 cm³

Now, we can use the formula for the volume of a cylinder to solve for the radius:

4.59 cm³ = πr²(2.00 cm)

Dividing both sides by π(2.00 cm), we get r² = 4.59 cm³ / (2.00 cm) ≈ 2.30 cm

Taking the square root of both sides, we find that r ≈ 1.52 cm.

Answer 2

find the volume of the cylinder using the mass and its density V = M / D
so Volume = 12.4 / 2.7 = 4.59259259259cm3

Divide by length to get the volume of a 1cm slice: 4.59259259259 / 2 = 2.2962962963

The cross section area in cm2 = the volume in cm3.

Reverse pi r^2 to get the radius, so divide by pi then take the square root.

R = √V / R = 0.85494667244cm

hope that helps