# 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?

Armorikam 2021-03-07 Answered
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?
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## Expert Answer

Sally Cresswell
Answered 2021-03-08 Author has 91 answers
Step 1
Diameter of 1st pump=5 cm
Diameter of 2nd pump=3 cm
Volume of 1st pump in one beat=$\pi {\left(\frac{5}{2}\right)}^{2}hc{m}^{3}=\pi {\left(\frac{5}{2}\right)}^{2}×1c{m}^{3}=\pi {\left(\frac{5}{2}\right)}^{2}c{m}^{3}$
Volume of 2st pump in one beat=$\pi {\left(\frac{3}{2}\right)}^{2}hc{m}^{3}=\pi {\left(\frac{3}{2}\right)}^{2}×1c{m}^{3}=\pi {\left(\frac{3}{2}\right)}^{2}c{m}^{3}$
Then extra blood pumped by 5 cm wide pump in one beat than a heart that in 3 cm wide=$\pi {\left(\frac{5}{2}\right)}^{2}-\pi {\left(\frac{3}{2}\right)}^{2}=\pi \left(\frac{25}{4}-\frac{9}{2}\right)=4\pi c{m}^{3}$
Step 2
Therefore extra volume of blood pumped $=4\pi c{m}^{3}$
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