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Biological tissues are typically made up of 98%water. Given that the density of water is 1.0×103kg/m3, estimate the mass of (a) the heart of an adult human; (b) a cell with a diameter of 0.5μm; (c) a honeybee.

Short Answer

Expert verified

a) Estimated mass of a human heart is 128.5g.

b) Estimated mass of a cell is 6.41×10-14g.

c) Estimated mass of the honeybee is 2.77g.

Step by step solution

01

Identification of given data

The given data is listed below,

  • Percentage of water content in biological tissues is98%.
  • The density of water is, ÒÏw=1.0×103kg/m3.
  • The diameter of the cell is, Dc=0.5μm10-6m1μm=0.5×10-6m.
02

Concept of the mass and density

The Objects have mass as they are made up of atoms, and atoms have mass as they are made up of fundamental particles- Protons, Electrons and Neutrons. Mass is a fundamental property of matter due to which a body undergoes gravitational interactions.

03

(a) Determination of the mass of the heart of an adult human

The size of the human heart can be estimated roughly as the size of a fist.

Assume its volume is (2in)3=8in3

Mass of human heart is given by,

m=ÒÏV

Here, ÒÏ is the density of water and V is the volume of the heart.

Substitute values in the above expression and using the information that 98% of the biological tissue is made up of water,

m=(0.98)1.0×103kg/m38in3=(0.98)8×103in3kg/m32.54cm1in31m100cm3=0.12847kg1000g1kg=128.5g

Thus, the mass of a human heart is estimated as 128.5g.

04

(b) Determination of the mass of a cell

Assume the cell as a sphere and therefore the volume of the cell is given by,

V=4Ï€3r3

Here, r is the radius of the sphere.

Substitute values in the above,

Vc=4π30.5×10-6m23=6.54×10-20m3

The mass of the cell is given by,

m=ÒÏV

Here, ÒÏ is the density of water and V is the volume of the cell.

Substitute values in the above and using the information that 98% of the biological tissue is made up of water,

mc=(0.98)1.0×103kg/m36.54×10-20m3=6.41×10-17kg1000g1kg=6.41×10-14g

Thus, the mass of a cell is estimated as 6.41×10-14g.

05

(c) Determination of the mass of a honeybee

Let the honeybee as a cylinder. and assume the length of the cylinder is 1cmand the radius is 3mm.

The volume of a cylinder is given by,

V=Ï€r2/

Here, r is the radius of the cylinder whose value is assumed as 1cm and l is the length of the cylinder whose value is assumed as 3mm

Substitute values in the above,

V=π(3cm)2(1mm)=π×9cm2×mm1m1000mm1m100cm2=2.83×10-6m3

The mass of the honeybee is given using the information that 98% of the biological tissue is made up of water,

m=(0.98)1×103kg/m32.83×10-6m3=2.77×10-3kg1000g1kg=2.77g

Thus, the mass of the honeybee will be 2.77g.

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