Understanding the Formula for the Volume of a Sphere

Oct 13, 2025 by miodeya.com 137 views

**What is the Exact Volume of a Sphere with a Radius of 7.5?**

Understanding the Formula for the Volume of a Sphere

The volume of a sphere is a fundamental concept in mathematics, and it is essential to understand the formula for calculating it. The formula for the volume of a sphere is given by:

V = (4/3)πr³

where V is the volume of the sphere, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sphere.

Calculating the Volume of a Sphere with a Radius of 7.5

To calculate the volume of a sphere with a radius of 7.5, we can plug the value of the radius into the formula:

V = (4/3)π(7.5)³

Step 1: Cubing the Radius

First, we need to cube the radius of the sphere:

(7.5)³ = 7.5 × 7.5 × 7.5 = 421.875

Step 2: Multiplying by π

Next, we multiply the result by π:

(4/3) × 3.14159 × 421.875 = 4,188.789

Step 3: Multiplying by 4/3

Finally, we multiply the result by 4/3:

(4/3) × 4,188.789 = 5,591.049

The Exact Volume of a Sphere with a Radius of 7.5

Therefore, the exact volume of a sphere with a radius of 7.5 is:

V = 5,591.049 units³

Frequently Asked Questions (FAQs)

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

Q: What is the value of π used in the formula?

A: The value of π used in the formula is approximately equal to 3.14159.

Q: How do I calculate the volume of a sphere with a given radius?

A: To calculate the volume of a sphere with a given radius, you can plug the value of the radius into the formula: V = (4/3)πr³

Q: What is the unit of measurement for the volume of a sphere?

A: The unit of measurement for the volume of a sphere is typically cubic units (e.g., units³).

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 plug in the value of the radius and the value of π, and the calculator will give you the result.

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

A: The formula for the volume of a sphere is significant because it allows us to calculate the volume of a sphere with a given radius, which is essential in various fields such as physics, engineering, and mathematics.

Q: Can I use the formula for the volume of a sphere to calculate the volume of other shapes?

A: No, the formula for the volume of a sphere is specific to spheres and cannot be used to calculate the volume of other shapes.

Q: What is the relationship between the radius and the volume of a sphere?

A: The radius of a sphere is directly proportional to the volume of the sphere. As the radius increases, the volume of the sphere also increases.

Q: Can I use the formula for the volume of a sphere to calculate the volume of a sphere with a negative radius?

A: No, the formula for the volume of a sphere is not defined for negative radii. The radius of a sphere must be a positive value.

Q: What is the significance of the constant π in the formula for the volume of a sphere?

A: The constant π is significant in the formula for the volume of a sphere because it represents the ratio of the circumference of a circle to its diameter.