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Chapter 1: Q91PP (page 65)

The human circulatory system is closed鈥攖hat is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. The blood in each of the heart鈥檚 four chambers comes briefly to rest before it is ejected by contraction of the heart muscle

If the aorta (diameter da) branches into two equal-sized arteries with a combined area equal to that of the aorta, what is the diameter of one of the branches? (a)d; (b)d2; (c)2d; (d)role="math" localid="1655806881203" da2

Short Answer

Expert verified

The diameter of one of the branches is, da2.

Step by step solution

01

Identification of given data

The given data can be listed below as-

  • The diameter of the aorta is,da.
02

Concept of area

Two-dimensional regions, shapes and planar lamina may all be described by their area in the plane.

The area of circle is given by,

A=蟺2鈥� (i)

03

Comparing initial area of arteries and final area of arteries

The area of the aorta is expressed as from the equation i),

A=蟺da22............. (ii)

Let, the diameter of one of the arteries is,

The area of the arteries can be expressed from the equation i),

A1=蟺d22

According to the question,, then the equation will be,

A=A1+A2A=2A1

Substituting the values in the equation (ii),

蟺da22=2蟺d22d=da2

Thus, the diameter of one of the branches is,da2.

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