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Volume of a Sphere

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Volume of a Sphere

Study Guide

Key Definition

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

Important Notes

The radius is half the diameter of the sphere.
$\pi$ can be approximated as 3.14 or left as $\pi$ in answers.
Volume is measured in cubic units such as $cm^3$ or $m^3$.
Ensure all measurements are in the same unit before calculating.
Practice converting diameter to radius.

Mathematical Notation

$\pi$ represents the mathematical constant Pi

$V$ represents volume

$r$ represents radius

$\frac{4}{3}$ represents the fraction four-thirds

$r^3$ represents the cube of the radius

Remember to use proper notation when solving problems

Why It Works

The formula is derived from integral calculus and represents the space a sphere occupies in three dimensions with $\frac{4}{3} \pi r^3$.

Remember

Always use $\frac{4}{3} \pi r^3$ to calculate the volume of a sphere and convert diameter to radius by dividing by 2.

Quick Reference

Volume Formula:$V = \frac{4}{3} \pi r^3$

Understanding Volume of a Sphere

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To find a sphere’s volume, cube the radius, multiply by π, then multiply by 4/3. In formula form: $V = \frac{4}{3} \pi r^3$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the volume of a sphere with a radius of $5$ cm?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you have a basketball with a diameter of $24$ cm. Find the volume.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If the volume of a sphere is $288\pi$ cubic units, find the radius.

Challenge Quiz

Single Choice Quiz

Advanced

The volume of a sphere is $500\pi$ cubic meters. What is the radius?

Recap

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Review key concepts and takeaways