volume of a sphere with a radius of 5
Understand the Problem
The question is asking for the calculation of the volume of a sphere given its radius, specifically 5 units. To solve this, we will use the formula for the volume of a sphere, which is (4/3) * π * r^3, where r is the radius.
Answer
The volume of the sphere is approximately $523.33$ cubic units.
Answer for screen readers
The volume of the sphere is approximately ( 523.33 ) cubic units.
Steps to Solve
- Identify the formula for volume of a sphere
We will use the formula for the volume of a sphere, which is given by:
$$ V = \frac{4}{3} \pi r^3 $$
where ( V ) is the volume and ( r ) is the radius.
- Substitute the radius into the formula
Now, we will substitute the given radius ( r = 5 ) into the formula:
$$ V = \frac{4}{3} \pi (5)^3 $$
- Calculate the cube of the radius
First, we will calculate ( 5^3 ):
$$ 5^3 = 125 $$
- Plug the value back into the equation
Now we substitute ( 125 ) back into our volume formula:
$$ V = \frac{4}{3} \pi (125) $$
- Multiply by ( \frac{4}{3} )
Now, we will calculate ( \frac{4}{3} \times 125 ):
$$ V = \frac{500}{3} \pi $$
- Final calculation
Finally, to find an approximate value for ( V ), we can use ( \pi \approx 3.14 ):
$$ V \approx \frac{500}{3} \times 3.14 $$
Calculating this gives:
$$ V \approx 523.33 $$
The volume of the sphere is approximately ( 523.33 ) cubic units.
More Information
The volume of a sphere can help us understand the capacity of three-dimensional objects. The formula shows how quickly the volume increases with the radius, as the radius is cubed. This concept is fundamental in geometry and is often used in various applications, including physics and engineering.
Tips
- Forgetting to cube the radius. Ensure that the radius is multiplied by itself three times.
- Confusing volume with surface area. Remember that this problem deals specifically with volume.
