Solved: "If hearts are geometrically similar and the volume..."

Armorikam

Answered question

2021-03-07

If hearts are geometrically similar and the volume of blood pumped in one beat is proportional to the volume of the heart, how much more blood will a heart 5 cm wide pump in one beat than a heart that is 3cm wide?

Answer & Explanation

Sally Cresswell

Skilled2021-03-08Added 91 answers

Step 1
Diameter of 1st pump=5 cm
Diameter of 2nd pump=3 cm
Volume of 1st pump in one beat=

π {(\frac{5}{2})}^{2} h c m^{3} = π {(\frac{5}{2})}^{2} \times 1 c m^{3} = π {(\frac{5}{2})}^{2} c m^{3}

Volume of 2st pump in one beat=

π {(\frac{3}{2})}^{2} h c m^{3} = π {(\frac{3}{2})}^{2} \times 1 c m^{3} = π {(\frac{3}{2})}^{2} c m^{3}

Then extra blood pumped by 5 cm wide pump in one beat than a heart that in 3 cm wide=

π {(\frac{5}{2})}^{2} - π {(\frac{3}{2})}^{2} = π (\frac{25}{4} - \frac{9}{2}) = 4 π c m^{3}

Step 2
Therefore extra volume of blood pumped

= 4 π c m^{3}

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