What is the volume of a sphere with radius 5?
Understand the Problem
The question is asking for the volume of a sphere given its radius. To find the volume, we will use the formula for the volume of a sphere, which is V = (4/3)πr³, where r is the radius.
Answer
The volume of the sphere is $$ V = \frac{500 \pi}{3} $$
Answer for screen readers
The volume of the sphere is
$$ V = \frac{500 \pi}{3} $$
Steps to Solve
- Identify the formula for the volume of a sphere
The formula to calculate the volume of a sphere is
$$ V = \frac{4}{3} \pi r^3 $$
where $V$ is the volume and $r$ is the radius of the sphere.
- Substitute the radius into the formula
After identifying the formula, substitute the value of the radius $r$ into the equation. For example, if the radius is given as $5$, the equation becomes:
$$ V = \frac{4}{3} \pi (5)^3 $$
- Calculate $r^3$
Calculate $5^3$:
$$ 5^3 = 125 $$
Now the equation looks like this:
$$ V = \frac{4}{3} \pi (125) $$
- Multiply by $\frac{4}{3}$
Now multiply $\frac{4}{3}$ by $125$:
$$ \frac{4 \times 125}{3} = \frac{500}{3} $$
- Multiply by $\pi$
Finally, multiply the result by $\pi$ to get the volume:
$$ V = \frac{500 \pi}{3} $$
This value is the volume of the sphere in terms of $\pi$.
The volume of the sphere is
$$ V = \frac{500 \pi}{3} $$
More Information
The volume of a sphere gives you a measure of how much space is contained within it. This formula is commonly used in geometry and can help in various applications, such as calculating materials required for making spheres or understanding natural objects like bubbles or planets.
Tips
- Forgetting to cube the radius when calculating volume.
- Incorrectly simplifying the fraction $\frac{4}{3}$.
- Not using $\pi$ in calculations or approximating it incorrectly.
