# 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?

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?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Sally Cresswell
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 $=4\pi c{m}^{3}$