Calculating the Mass of Low-Density Lipoprotein in a Cylinder

Question:

What mass of low-density lipoprotein is contained in a cylinder that is 1.25 cm long and 0.50 cm in diameter?

Answer:

To find the mass of low-density lipoprotein in the cylinder, calculate the cylinder's volume and multiply it by the density of LDL (1.04 g/cm³), which gives approximately 0.255 grams.

Explanation:

Low-Density Lipoprotein (LDL) Mass Calculation:

To calculate the mass of low-density lipoprotein (LDL) in a cylinder, we first determine the cylinder's volume and then use the provided density to find the mass. The LDL is contained in a cylinder that is 1.25 cm long with a diameter of 0.50 cm. The density of LDL is given as 1.04 g/cm³.

First, we calculate the volume of the cylinder using the formula for the volume of a cylinder, V = πr²h, where r is the radius (half of the diameter) and h is the height. The radius r = 0.50 cm / 2 = 0.25 cm, and the height h = 1.25 cm. So, V = π(0.25 cm)²(1.25 cm).

Volume, V = π(0.0625 cm²)(1.25 cm) = π(0.078125 cm³) ≈ 0.245 cm³.

Now, using the density of LDL, we calculate the mass by multiplying the volume by the density: Mass = Density × Volume. Thus, Mass = 1.04 g/cm³ × 0.245 cm³ = 0.255 g (approximately).

The mass of low-density lipoprotein contained in the given cylinder is approximately 0.255 grams.

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