A Sphere Has A Diameter Of 10 In. What Is The Volume Of The Sphere?A. V = 125 3 V=\frac{125}{3} V = 3 125 ​ In { ^3$}$ B. V = 500 3 V=\frac{500}{3} V = 3 500 ​ In { ^3$}$ C. V = 500 3 Π V=\frac{500}{3} \pi V = 3 500 ​ Π In { ^2$}$ D. $V=\frac{4000}{3}

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 given diameter.

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

To calculate the volume of a sphere, we need to know its radius. The radius of a sphere is half of its diameter. Given that the diameter of the sphere is 10 inches, we can calculate the radius as follows:

r = diameter / 2 r = 10 / 2 r = 5 inches

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.

V = (4/3)π(5)^3 V = (4/3)π(125) V = (4/3)(3.14159)(125) V = 523.5987756

Simplifying the Answer

The answer we obtained is a decimal value. However, we can simplify it by expressing it as a fraction.

Q&A: Calculating the Volume of a Sphere

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 know its diameter. The radius is half of the diameter. So, if the diameter is 10 inches, the radius is 5 inches.

Q: What is the volume of a sphere with a diameter of 10 inches?

A: To calculate the volume of a sphere with a diameter of 10 inches, we need to use the formula V = (4/3)πr^3. Since the radius is 5 inches, we can plug in the values as follows:

V = (4/3)π(5)^3 V = (4/3)π(125) V = (4/3)(3.14159)(125) V = 523.5987756

Q: How do I simplify the answer?

A: The answer we obtained is a decimal value. However, we can simplify it by expressing it as a fraction. To do this, we can divide the numerator and denominator by their greatest common divisor.

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