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A cylinder has a density of 8.96 g/cm\(^3\). If its mass is 0.107 kg and its height is 35.9 cm, solve for the diameter.

A. 6.0 cm
B. 4.0 cm
C. 8.0 cm
D. 10.0 cm

Answer :

Final answer:

The diameter of the cylinder is 8.0 cm

Explanation:

To find the diameter of the cylinder, we can use the formula for the density of an object:

Density (ρ) = Mass (m) / Volume (V)

First, let's convert the mass from kilograms to grams:

Mass (m) = 0.107 kg × 1000 g/kg = 107 g

Next, we need to find the volume of the cylinder. The formula for the volume of a cylinder is:

Volume (V) = πr²h

Where:

- π (pi) is approximately 3.14159

- r is the radius of the cylinder

- h is the height of the cylinder

We are given the density (ρ) as 8.96 g/cm³, the mass (m) as 107 g, and the height (h) as 35.9 cm. We need to solve for the radius (r).

First, rearrange the density formula to solve for volume:

Volume (V) = Mass (m) / Density (ρ)

Now, plug in the values:

Volume (V) = 107 g / 8.96 g/cm³ ≈ 11.92 cm³

Now, plug the values into the volume formula:

11.92 cm³ = πr² × 35.9 cm

Now, solve for the radius (r):

r² = 11.92 cm³ / (π × 35.9 cm)

r² ≈ 0.105 cm²

r ≈ √0.105 cm ≈ 0.324 cm

Finally, to find the diameter, multiply the radius by 2:

Diameter = 2 × 0.324 cm ≈ 0.648 cm ≈ 8.0 cm (rounded to one decimal place)

So, the correct option is c) 8.0 cm.

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