This Sphere Has A Diameter Of 5 M.What Is The Volume Of The Sphere?A. V = 9 2 Π M 3 V=\frac{9}{2} \pi \, \text{m}^3 V = 2 9 Π M 3 B. V = 125 6 Π M 3 V=\frac{125}{6} \pi \, \text{m}^3 V = 6 125 Π M 3 C. V = 500 3 Π M 3 V=\frac{500}{3} \pi \, \text{m}^3 V = 3 500 Π M 3 D. $V=\frac{4000}{3} \pi ,
Introduction
In mathematics, the volume of a sphere is a fundamental concept that is used to calculate the amount of space inside a sphere. The formula for the volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere. In this article, we will use this formula to calculate the volume of a sphere with a diameter of 5 m.
Understanding the Formula
The formula for the volume of a sphere is V = (4/3)πr^3. This formula is derived from the fact that the volume of a sphere is proportional to the cube of its radius. The constant of proportionality is (4/3)π.
Calculating the Radius
The radius of a sphere is half of its diameter. Since the diameter of the sphere is 5 m, the radius is 5/2 = 2.5 m.
Calculating the Volume
Now that we have the radius, we can calculate the volume of the sphere using the formula V = (4/3)πr^3.
import math
r = 2.5
V = (4/3) * math.pi * (r ** 3)
print(V)
Simplifying the Answer
The answer to the above code is V = (4/3)π(2.5)^3 = (4/3)π(15.625) = (4/3) * 49.087 = 65.459. However, this is not among the options. We need to simplify the answer to match one of the options.
Simplifying the Answer: Part 2
Let's simplify the answer further by multiplying the numerator and denominator by 125.
import math
r = 2.5
V = (4/3) * math.pi * (r ** 3)
V = (4/3) * math.pi * (2.5 ** 3)
V = (4/3) * math.pi * (15.625)
V = (4/3) * math.pi * (125/8)
V = (500/3) * math.pi
print(V)
Conclusion
In conclusion, the volume of the sphere with a diameter of 5 m is V = (500/3)π m^3. This is option C.
Final Answer
Q: What is the formula for the volume of a sphere?
A: The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
Q: How do I calculate the radius of a sphere?
A: To calculate the radius of a sphere, you need to divide the diameter of the sphere by 2. For example, if the diameter of the sphere is 5 m, the radius is 5/2 = 2.5 m.
Q: What is the relationship between the diameter and the radius of a sphere?
A: The radius of a sphere is half of its diameter. This means that if you know the diameter of a sphere, you can easily calculate its radius by dividing the diameter by 2.
Q: Can I use the formula V = (4/3)πr^3 to calculate the volume of a sphere with a diameter of 10 m?
A: Yes, you can use the formula V = (4/3)πr^3 to calculate the volume of a sphere with a diameter of 10 m. First, calculate the radius by dividing the diameter by 2: r = 10/2 = 5 m. Then, plug the value of r into the formula: V = (4/3)π(5)^3 = (4/3)π(125) = (500/3)π m^3.
Q: What if I want to calculate the volume of a sphere with a diameter of 20 m?
A: To calculate the volume of a sphere with a diameter of 20 m, first calculate the radius by dividing the diameter by 2: r = 20/2 = 10 m. Then, plug the value of r into the formula: V = (4/3)π(10)^3 = (4/3)π(1000) = (4000/3)π m^3.
Q: Can I use a calculator to calculate the volume of a sphere?
A: Yes, you can use a calculator to calculate the volume of a sphere. Simply enter the value of the radius into the calculator and use the formula V = (4/3)πr^3 to calculate the volume.
Q: What if I want to calculate the volume of a sphere with a diameter of 15 m?
A: To calculate the volume of a sphere with a diameter of 15 m, first calculate the radius by dividing the diameter by 2: r = 15/2 = 7.5 m. Then, plug the value of r into the formula: V = (4/3)π(7.5)^3 = (4/3)π(421.875) = (1750/3)π m^3.
Q: Can I use a spreadsheet to calculate the volume of a sphere?
A: Yes, you can use a spreadsheet to calculate the volume of a sphere. Simply enter the value of the radius into the spreadsheet and use the formula V = (4/3)πr^3 to calculate the volume.
Conclusion
In conclusion, calculating the volume of a sphere is a simple process that involves using the formula V = (4/3)πr^3 and plugging in the value of the radius. With a little practice, you can easily calculate the volume of a sphere with any diameter.