Answer:
0.58 m²/100 g
Explanation:
Let us consider a chunk of muscle with a cross-sectional area of 1 mm² and which 500m long. If this chunk contain 250 capillaries and each with 4m radius long .
Now if we calculate the muscle slab weight along with the surface area of capillaries in the muscles. To calculate the surface area per unit weight of muscle we will neee to divide the surface area of capillaries that are there in the muscle to the area by the mass of the muscle long.
This slab of muscle contains 250 capillaries with a radius of 4m each. We calculate how much this muscle slab weighs,
how much surface area of capillaries there are in the muscle,
and then we will divide the area by the mass of the muscle to find the surface area per unit weight of muscle
The volume of the piece of muscle is;
=1 mm² x 500 x 10⁻⁶ m
= 1 mm² x 0.5 mm
= 0.5 mm³
Now since 1cm = 1000mm
Therefore, the volume will be equal to
= 0.5 x 10⁻³ cm³
And its mass is 0.5 x 10 ⁻³ cm³ x 1.08 g cm⁻³
= 0.54 x 10⁻³ g
surface area of a single capillary is = 2B × r × l
where;
r = radius, l = length
∴ surface area = 2 B x 4 x 10⁻⁶ m x 500 x 10⁻⁶ m
= 12566 x 10⁻¹² m²
Now for 250 capillaries the total surface area is 250 x 12566 x 10⁻¹² m²
= 3141500 x 10⁻¹² m² in a mass of muscle that weighs 0.54 x 10⁻³ g.
So the surface area of capillaries is 3.1415 x 10⁻⁶ m²/ 0.54 x 10⁻³ g
= 5.818 x 10⁻³ m² g⁻¹ x 1 g /100 g
= 0.58 m²/100 g
