The DNA of an E coli cell measures 1.4 mm in length, when extended and 20 angstroms in diameter.
a) Calculate the volume of DNA in an E coli cell in cm^3
b) What fraction of an E coli cell is occupied by its DNA?
c) A human cell is typically spherical with a diameter of 20 micrometers. Calculate the volume of a human cell in cm ^3.
1.4 mm = 0.14 cm
20 angstroms = 20 x 10^-8 cm.
Use those dimensions to determine the volume.
Do you know the volume of an E coli cell? Don't you need to know that before b can be answered.
For c, 20 micrometers = 20 x 10^-4 cm
Post your work if you get stuck.
To calculate these values, we need to use some conversion factors.
1 mm = 10^-1 cm
1 Å = 10^-8 cm
1 μm = 10^-4 cm
a) To calculate the volume of DNA in an E. coli cell in cm^3, we will use the formula for the volume of a cylinder:
Volume of DNA = π * (radius)^2 * length
Given that the length is 1.4 mm and the radius is half of the diameter (20 Å), we need to convert the measurements to cm:
Length = 1.4 mm * 10^-1 cm/mm = 0.14 cm
Diameter = 20 Å * 10^-8 cm/Å = 2 * 10^-6 cm
Radius = 1 * 10^-6 cm
Volume of DNA = π * (1 * 10^-6 cm)^2 * 0.14 cm
≈ 4 * 10^-14 cm^3
b) To find the fraction of an E. coli cell occupied by its DNA, we need to divide the volume of DNA by the total cell volume. For simplicity, let's assume an E. coli cell is a cylinder with the same diameter as the DNA.
Total cell volume = π * (radius)^2 * length
Using the same conversion factors, we have:
Diameter = 20 Å * 10^-8 cm/Å = 2 * 10^-6 cm
Radius = 1 * 10^-6 cm
Length = length of DNA = 0.14 cm
Total cell volume = π * (1 * 10^-6 cm)^2 * 0.14 cm
≈ 4 * 10^-14 cm^3
The fraction of the E. coli cell occupied by its DNA is:
Fraction = Volume of DNA / Total cell volume
≈ (4 * 10^-14 cm^3) / (4 * 10^-14 cm^3)
= 1
So, the entire E. coli cell is occupied by its DNA.
c) To calculate the volume of a human cell, which is typically spherical, we use the formula for the volume of a sphere:
Volume of sphere = (4/3) * π * (radius)^3
Given that the diameter of a human cell is 20 μm, we need to convert it to cm:
Diameter = 20 μm * 10^-4 cm/μm = 2 * 10^-2 cm
Radius = (1/2) * (2 * 10^-2 cm) = 1 * 10^-2 cm
Volume of human cell = (4/3) * π * (1 * 10^-2 cm)^3
≈ 4.19 * 10^-3 cm^3
To calculate the volume of DNA in an E. coli cell and the volume of a human cell, we need to use the formulas for the volume of a cylinder and a sphere, respectively.
a) Calculate the volume of DNA in an E. coli cell in cm^3:
Given:
Length of DNA = 1.4 mm = 0.14 cm
Diameter of DNA = 20 angstroms = 2 x 10^-6 cm
The volume of a cylinder is given by the formula:
V_cylinder = π * (r^2) * h
Where:
π ≈ 3.14159 (pi)
r = radius of the cylinder = diameter/2 = (2 x 10^-6 cm) / 2 = 10^-6 cm
h = height/length of the cylinder = 0.14 cm
Substituting the values into the formula:
V_cylinder = 3.14159 * (10^-6 cm)^2 * 0.14 cm
≈ 4.39 x 10^-15 cm^3
Therefore, the volume of DNA in an E. coli cell is approximately 4.39 x 10^-15 cm^3.
b) What fraction of an E. coli cell is occupied by its DNA:
To find the fraction of an E. coli cell occupied by its DNA, we need to divide the volume of DNA by the total volume of the E. coli cell.
Given:
Volume of DNA = 4.39 x 10^-15 cm^3
E. coli cells are prokaryotic cells, which are generally smaller compared to eukaryotic cells. Although the average size of an E. coli cell can vary, for the purpose of this calculation, let's assume its diameter is around 1 μm (10^-4 cm).
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * (radius^3)
Where:
π ≈ 3.14159 (pi)
radius = diameter/2 = (10^-4 cm) / 2 = 5 x 10^-5 cm
Substituting the values into the formula:
V_sphere = (4/3) * 3.14159 * (5 x 10^-5 cm)^3
≈ 5.24 x 10^-14 cm^3
Now, calculating the fraction of the E. coli cell occupied by its DNA:
Fraction = Volume of DNA / Volume of E. coli cell
= (4.39 x 10^-15 cm^3) / (5.24 x 10^-14 cm^3)
≈ 0.0839
Therefore, the fraction of the E. coli cell occupied by its DNA is approximately 0.0839, which is about 8.39%.
c) Calculate the volume of a human cell in cm ^3:
Given:
Diameter of human cell = 20 μm = 2 x 10^-3 cm
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * (radius^3)
Where:
π ≈ 3.14159 (pi)
radius = diameter/2 = (2 x 10^-3 cm) / 2 = 10^-3 cm
Substituting the values into the formula:
V_sphere = (4/3) * 3.14159 * (10^-3 cm)^3
≈ 4.19 x 10^-9 cm^3
Therefore, the volume of a human cell is approximately 4.19 x 10^-9 cm^3.