One cubic centimetre (1.0 cm3) of water has a mass of 1.0 × 10−3 kg. (a) Determine the mass of
1.0 litre of water. Assuming that biological substances are 98% water, estimate the masses of (b) a cell with a diameter of 1.0 μm, (c) a human kidney, and (d) a fly. Assume the cell to be spherical, take a kidney to be roughly a sphere with a radius of 3.5 cm and a fly to be roughly a cylinder 3.8 mm long and 1.7 mm in diameter.
a. 0.03L = 1 oz.
L = 33.4 oz.
M = 0.454kg/16oz * 33.4oz = 0.948 kg.
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To solve this problem, we need to use the given density of water and apply it to different volumes to find the masses.
(a) To determine the mass of 1.0 liter of water, we need to convert the volume to cubic meters (m3) because the density is given in kilograms per cubic meter (kg/m3). Since 1 liter is equal to 0.001 cubic meters (m3), we can calculate the mass using the formula:
Mass = Density x Volume
Mass = 1000 kg/m3 x 0.001 m3 = 1 kg
Therefore, 1.0 liter of water has a mass of 1.0 kg.
(b) To estimate the mass of a cell with a diameter of 1.0 μm, we can approximate it as a sphere. The formula to calculate the volume of a sphere is:
Volume = (4/3)πr^3
where r is the radius of the sphere. The radius can be calculated by dividing the diameter by 2:
r = 1.0 μm / 2 = 0.5 μm
Now, we convert the radius to meters:
r = 0.5 μm x 10^-6 m/μm = 0.5 x 10^-6 m
Using this radius, we can find the volume:
Volume = (4/3)π(0.5 x 10^-6 m)^3
After calculating the volume, we can find the mass by multiplying it by the density of water (1.0 × 10−3 kg/cm3):
Mass = Volume x Density = Volume x 1.0 × 10−3 kg/cm3
(c) To estimate the mass of a human kidney, we can approximate it as a sphere with a given radius of 3.5 cm. We can use the same formula mentioned above to calculate the volume of the sphere:
Volume = (4/3)π(3.5 cm)^3
Again, after calculating the volume, we can find the mass by multiplying it by the density of water (1.0 × 10−3 kg/cm3).
(d) To estimate the mass of a fly, we can approximate its shape as a cylinder. The length of the fly is given as 3.8 mm, and the diameter is given as 1.7 mm. The formula to calculate the volume of a cylinder is:
Volume = πr^2h
where r is the radius of the cylinder and h is the height.
To calculate the radius, we divide the diameter by 2:
r = 1.7 mm / 2 = 0.85 mm
Now, we convert the radius to meters:
r = 0.85 mm x 10^-3 m/mm = 0.85 x 10^-3 m
Using this radius, we can find the volume:
Volume = π(0.85 x 10^-3 m)^2 x 3.8 x 10^-3 m
Again, after calculating the volume, we can find the mass by multiplying it by the density of water (1.0 × 10−3 kg/cm3).
By following these steps, you can calculate the masses of a cell with a diameter of 1.0 μm, a human kidney, and a fly using the given density of water and their respective volumes.