The Radius Of A Sphere Changes From 5 Cm To 7 Cm. By How Much Has Its Volume Changed, In Cm³?

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The radius of a sphere changes from 5 cm to 7 cm. By how much has its volume changed, in cm³?

The problem involves finding the change in volume of a sphere when its radius changes from 5 cm to 7 cm. To solve this problem, we need to use the formula for the volume of a sphere, which is given by:

V = (4/3)πr³

where V is the volume of the sphere and r is its radius.

Calculating the Initial Volume

First, let's calculate the initial volume of the sphere with a radius of 5 cm.

import math

# Define the radius of the sphere
r_initial = 5  # in cm

# Calculate the initial volume
V_initial = (4/3) * math.pi * (r_initial ** 3)
print("Initial Volume:", V_initial, "cm³")

Calculating the Final Volume

Next, let's calculate the final volume of the sphere with a radius of 7 cm.

# Define the radius of the sphere
r_final = 7  # in cm

# Calculate the final volume
V_final = (4/3) * math.pi * (r_final ** 3)
print("Final Volume:", V_final, "cm³")

Finding the Change in Volume

Now that we have the initial and final volumes, we can find the change in volume by subtracting the initial volume from the final volume.

# Calculate the change in volume
ΔV = V_final - V_initial
print("Change in Volume:", ΔV, "cm³")

Analyzing the Results

Let's analyze the results of our calculations.

Radius (cm) Volume (cm³)
5 523.5987755982988
7 1436.7550479459053
ΔV 913.1562723476065

As we can see, the volume of the sphere has increased by 913.156 cm³ when its radius changes from 5 cm to 7 cm.

Conclusion

In this article, we have calculated the change in volume of a sphere when its radius changes from 5 cm to 7 cm. We used the formula for the volume of a sphere and calculated the initial and final volumes using Python. We then found the change in volume by subtracting the initial volume from the final volume. The results show that the volume of the sphere has increased by 913.156 cm³.

References

Further Reading

If you want to learn more about the volume of a sphere, I recommend checking out the following resources:

Code

import math

def calculate_volume(radius):
    return (4/3) * math.pi * (radius ** 3)

def main():
    r_initial = 5  # in cm
    r_final = 7  # in cm

    V_initial = calculate_volume(r_initial)
    V_final = calculate_volume(r_final)

    ΔV = V_final - V_initial

    print("Initial Volume:", V_initial, "cm³")
    print("Final Volume:", V_final, "cm³")
    print("Change in Volume:", ΔV, "cm³")

if __name__ == "__main__":
    main()
```<br/>
**The radius of a sphere changes from 5 cm to 7 cm. By how much has its volume changed, in cm³? - Q&A**

**Understanding the Problem**
==========================

The problem involves finding the change in volume of a sphere when its radius changes from 5 cm to 7 cm. To solve this problem, we need to use the formula for the volume of a sphere, which is given by:

**V = (4/3)πr³**

where V is the volume of the sphere and r is its radius.

**Q: What is the formula for the volume of a sphere?**
----------------------------------------------

A: The formula for the volume of a sphere is given by:

**V = (4/3)πr³**

where V is the volume of the sphere and r is its radius.

**Q: How do I calculate the initial volume of the sphere?**
---------------------------------------------------

A: To calculate the initial volume of the sphere, you need to use the formula:

**V = (4/3)πr³**

where V is the volume of the sphere and r is its radius. In this case, the radius is 5 cm.

```python
import math

# Define the radius of the sphere
r_initial = 5  # in cm

# Calculate the initial volume
V_initial = (4/3) * math.pi * (r_initial ** 3)
print("Initial Volume:", V_initial, "cm³")

Q: How do I calculate the final volume of the sphere?

A: To calculate the final volume of the sphere, you need to use the formula:

V = (4/3)πr³

where V is the volume of the sphere and r is its radius. In this case, the radius is 7 cm.

# Define the radius of the sphere
r_final = 7  # in cm

# Calculate the final volume
V_final = (4/3) * math.pi * (r_final ** 3)
print("Final Volume:", V_final, "cm³")

Q: How do I find the change in volume of the sphere?

A: To find the change in volume of the sphere, you need to subtract the initial volume from the final volume.

# Calculate the change in volume
ΔV = V_final - V_initial
print("Change in Volume:", ΔV, "cm³")

Q: What is the change in volume of the sphere?

A: The change in volume of the sphere is 913.156 cm³.

Q: Can I use a calculator to find the change in volume of the sphere?

A: Yes, you can use a calculator to find the change in volume of the sphere. Simply enter the values of the initial and final volumes and subtract them.

Q: Can I use a spreadsheet to find the change in volume of the sphere?

A: Yes, you can use a spreadsheet to find the change in volume of the sphere. Simply enter the values of the initial and final volumes and subtract them.

Q: What is the significance of the change in volume of the sphere?

A: The change in volume of the sphere is significant because it represents the change in the amount of material in the sphere. In this case, the sphere has increased in volume by 913.156 cm³.

Conclusion

In this article, we have answered some common questions related to the change in volume of a sphere when its radius changes from 5 cm to 7 cm. We have used the formula for the volume of a sphere and calculated the initial and final volumes using Python. We have then found the change in volume by subtracting the initial volume from the final volume. The results show that the volume of the sphere has increased by 913.156 cm³.

References

Further Reading

If you want to learn more about the volume of a sphere, I recommend checking out the following resources:

Code

import math

def calculate_volume(radius):
    return (4/3) * math.pi * (radius ** 3)

def main():
    r_initial = 5  # in cm
    r_final = 7  # in cm

    V_initial = calculate_volume(r_initial)
    V_final = calculate_volume(r_final)

    ΔV = V_final - V_initial

    print("Initial Volume:", V_initial, "cm³")
    print("Final Volume:", V_final, "cm³")
    print("Change in Volume:", ΔV, "cm³")

if __name__ == "__main__":
    main()