Volume of a sphere

Definition

The volume of a sphere is the measure of the amount of space inside the sphere, calculated using the formula $V = \frac{4}{3} \pi r^3$, where $r$ is the radius.

5 Must Know Facts For Your Next Test

1. To find the volume of a sphere, you need to know its radius.
2. The formula $V = \frac{4}{3} \pi r^3$ involves multiplying by $\pi$, which can be approximated as 3.14159.
3. Volume grows rapidly with an increase in radius due to the cubic relationship.
4. In polynomial functions, the term $r^3$ indicates a power function of degree 3.
5. Understanding how to derive and manipulate polynomial expressions is critical for solving problems related to the volume of a sphere.

Review Questions

• What is the formula for calculating the volume of a sphere?
• How does changing the radius affect the volume of a sphere?
• Explain why $r^3$ in the volume formula represents a polynomial function.

Related terms

Radius: The distance from the center of a sphere to any point on its surface.

Polynomial Function: A mathematical expression that involves sums and products of variables raised to whole number exponents.

$\pi$ (Pi): A mathematical constant representing the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.