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The human heartbeat, as determined by the pulse rate, is normally about 60 beats \(/ \mathrm{min}\). If the heart pumps \(75 \mathrm{~mL}\) of blood per beat, what volume of blood is pumped in one day in liters?

Short Answer

Expert verified
The heart pumps 6480 liters of blood per day.

Step by step solution

01

Calculate Beats per Day

First, we need to determine how many heartbeats occur in a single day. We know the heartbeat rate is 60 beats per minute, and there are 1440 minutes in a day (24 hours * 60 minutes). Thus, the number of beats per day is given by:\[ 60 ext{ beats/minute} \times 1440 ext{ minutes/day} = 86400 ext{ beats/day} \]
02

Calculate Volume of Blood Pumped Per Day

Now that we have the total number of beats per day, we can calculate the total volume of blood pumped per day. If the heart pumps 75 mL of blood per beat, the total volume in milliliters per day is:\[ 75 ext{ mL/beat} \times 86400 ext{ beats/day} = 6480000 ext{ mL/day} \]
03

Convert Milliliters to Liters

Finally, we need to convert the volume from milliliters to liters, knowing that 1000 mL = 1 L. Therefore, the volume in liters is:\[ \frac{6480000 ext{ mL}}{1000} = 6480 ext{ L} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mathematical Problem-Solving
When approaching mathematical problems, clear step-by-step strategies are essential. In the problem of calculating the volume of blood pumped in a day, we start by identifying the fundamental elements involved and the sequence of calculations needed.
The solution begins with understanding the heartbeat frequency, expressed in beats per minute. Evaluating such problems involves breaking them down into smaller, manageable parts:
  • First, establish the number of heartbeats in a certain time frame by utilizing the given rate.
  • Translate this understanding into the daily heartbeat count.
  • Subsequently, link each heartbeat to a specific volume of blood.
By systematically adding and calculating each of these steps, complex problems become much more approachable.
Problem-solving requires not only mathematical computations but also logical reasoning to apply the correct formulas and unit conversions effectively. It helps to keep track of units at every step, ensuring that the final result is coherent and correctly aligned with the question's requirements.
Volume Measurement
Volume measurement is a crucial concept in many scientific calculations, including physiology and everyday mathematics. In this context, we're dealing with blood volume, which is initially measured in milliliters per heartbeat.
Understanding the measurement units and conversion processes is vital:
  • Volume is first calculated in milliliters, depicting short-term, immediate measurements.
  • This value is then translated into a larger scale by summing the daily measurements.
  • Finally, conversion from milliliters to liters is achieved through a simple conversion factor (1000 mL = 1 L).
These steps demonstrate a simple yet effective volume measurement model, applicable across numerous scientific and real-world scenarios.
Anywhere you see volume measurements, remember that accurate unit conversion remains integral to accuracy—especially when conclusions are drawn from these numeric results.
Heart Physiology
The heart's physiology involves complex mechanical and chemical processes within the human body. It's fascinating how the heart functions like a pump, pushing blood not just consistently, but efficiently throughout the day.
A few relevant insights about heart physiology include:
  • The heart rate, typically quantified as beats per minute, informs us of the heart's activity level.
  • Each beat propels a specific volume of blood, signaling how well the heart supplies oxygen and nutrients.
  • Over extended periods, such as a day, the heart works tirelessly, showcasing its endurance by pumping a massive volume of blood.
Understanding these physiology basics helps appreciate the heart's role in maintaining health and reflecting overall fitness.
Integrating anatomy with mathematical calculations allows us to visualize how much vital resource—blood—is managed by our heart every day, underscoring its essential function in sustaining life.

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