Find the volume of a sphere of radius 3 cm.
Understand the Problem
The question is asking us to calculate the volume of a sphere given its radius, which is 3 cm. To solve this, we will use the formula for the volume of a sphere, V = (4/3)πr³, where r is the radius.
Answer
The volume of the sphere is approximately \( 113.04 \, \text{cm}^3 \).
Answer for screen readers
The volume of the sphere is approximately ( 113.04 , \text{cm}^3 ).
Steps to Solve
- Formula for Volume of a Sphere
To find the volume ( V ) of a sphere, use the formula:
$$ V = \frac{4}{3} \pi r^3 $$
where ( r ) is the radius.
- Substituting the Given Value
Substitute the radius ( r = 3 , \text{cm} ) into the formula:
$$ V = \frac{4}{3} \pi (3)^3 $$
- Calculating ( (3)^3 )
Calculate ( (3)^3 ):
$$ (3)^3 = 27 $$
- Final Calculation
Now plug ( 27 ) back into the equation:
$$ V = \frac{4}{3} \pi (27) $$
- Simplifying the Expression
Multiply:
$$ V = 36 \pi $$
- Using Approximation for (\pi)
If needed, use ( \pi \approx 3.14 ):
$$ V \approx 36 \times 3.14 $$
- Final Volume
Calculate the approximate volume:
$$ V \approx 113.04 , \text{cm}^3 $$
The volume of the sphere is approximately ( 113.04 , \text{cm}^3 ).
More Information
The volume of a sphere is an important concept in geometry and is applicable in various real-world scenarios, such as in determining the capacity of spherical objects.
Tips
- Incorrectly calculating the cube: Ensure that when finding ( r^3 ), the number is multiplied correctly (e.g., ( 3 \times 3 \times 3 )).
- Neglecting to multiply by (\frac{4}{3}): Always remember the fraction in the volume formula.
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