one cubic meter of water hass a mass of 1.0x10^-3. (a) determine the mass of 1.0 m^3. (b) assu!ing biological substance are 98% water, estimate the mass of cell with a 1.0 micrometer dia!eter, a human kidney and a fly. assume a kidney is roughly a sphere with radius of 4.0 cm, and a fly is roughly a cylinder 4.0 mm long and 2.0 mm in diameter

your first statement...hass a mass of ... what are the units of that number, as it makes no sense.

To determine the mass of 1.0 m^3 of water, you can use the given information about the mass of 1 cubic meter.

(a) The mass of 1 cubic meter of water is given as 1.0x10^-3. This means that 1 cubic meter has a mass of 0.001 kilograms (since 1 gram = 0.001 kilograms).

So, the mass of 1.0 m^3 of water is 0.001 kilograms.

Now, let's move on to estimating the masses of biological substances.

(b) To calculate the mass of a cell, we need to consider that it is 98% water. You don't have an exact shape of the cell, but based on the given diameter of 1.0 micrometers, let's assume it's roughly spherical.

The formula to calculate the volume of a sphere is V = (4/3)πr^3, where r is the radius.

Given the diameter of 1.0 micrometer, the radius (r) would be 0.5 micrometers (since radius = diameter/2).

Converting micrometers to meters:
0.50 micrometers = 0.50 x 10^-6 meters = 5.0 x 10^-7 meters

Now, let's calculate the volume of the cell:
V = (4/3)π(5.0 x 10^-7)^3 = 5.24 x 10^-19 cubic meters

Since the cell is 98% water, the mass of the cell can be calculated by:
Mass = Volume x Density (density of water = 1.0x10^-3 kg/m^3)

Mass = 5.24 x 10^-19 cubic meters x 1.0x10^-3 kg/m^3 = 5.24 x 10^-22 kilograms

The estimated mass of the cell is 5.24 x 10^-22 kilograms.

Now, let's move on to estimating the mass of a human kidney.

A kidney is roughly spherical with a radius of 4.0 cm.
Converting centimeters to meters:
4.0 cm = 4.0 x 10^-2 meters

Using the formula to calculate the volume of a sphere:
V = (4/3)π(4.0 x 10^-2)^3 = 0.0335 cubic meters

Since a kidney is roughly 98% water, the mass of the kidney can be calculated by:
Mass = Volume x Density (density of water = 1.0x10^-3 kg/m^3)

Mass = 0.0335 cubic meters x 1.0x10^-3 kg/m^3 = 3.35 x 10^-5 kilograms

The estimated mass of a human kidney is 3.35 x 10^-5 kilograms.

Next, let's estimate the mass of a fly.

Assuming the fly is roughly a cylinder, we can calculate its volume and then determine its mass.

The length of the fly is given as 4.0 mm and the diameter is 2.0 mm.
Converting millimeters to meters:
4.0 mm = 4.0 x 10^-3 meters
2.0 mm = 2.0 x 10^-3 meters

Using the formula to calculate the volume of a cylinder:
V = πr^2h, where r is the radius and h is the height.

Since the diameter is given, the radius (r) would be 1.0 mm (or 1.0 x 10^-3 meters).

Calculating the volume of the cylinder:
V = π(1.0 x 10^-3)^2(4.0 x 10^-3) = 1.57 x 10^-8 cubic meters

Since the fly is 98% water, we can calculate its mass by:
Mass = Volume x Density (density of water = 1.0x10^-3 kg/m^3)

Mass = 1.57 x 10^-8 cubic meters x 1.0x10^-3 kg/m^3 = 1.57 x 10^-11 kilograms

The estimated mass of the fly is 1.57 x 10^-11 kilograms.

So, the estimated masses are as follows:
- Cell: 5.24 x 10^-22 kilograms
- Kidney: 3.35 x 10^-5 kilograms
- Fly: 1.57 x 10^-11 kilograms