Volume of a sphere with radius 5.
Understand the Problem
The question is asking for the volume of a sphere given its radius, which is 5 units. 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 is \( \frac{500}{3} \pi \) cubic units.
Answer for screen readers
The volume of the sphere is ( \frac{500}{3} \pi ) cubic units.
Steps to Solve
- Identify the radius
The radius (r) of the sphere is given as 5 units.
- Use the volume formula
Substitute the radius into the volume formula for a sphere: $$ V = \frac{4}{3} \pi r^3 $$
- Calculate the volume
Plug in the radius into the equation: $$ V = \frac{4}{3} \pi (5)^3 $$
- Simplify the calculation
First, calculate ( 5^3 ): $$ 5^3 = 125 $$
Next, substitute that back into the volume formula: $$ V = \frac{4}{3} \pi (125) $$
- Final computation
Multiply ( \frac{4}{3} ) by 125: $$ V = \frac{500}{3} \pi $$
The volume of the sphere is ( \frac{500}{3} \pi ) cubic units.
More Information
The volume of a sphere increases with the cube of the radius. This means even a small increase in radius can lead to a large increase in volume.
Tips
- Forgetting to cubed the radius when substituting it into the formula can lead to incorrect calculations. Ensure that you calculate ( r^3 ) correctly before multiplying by ( \frac{4}{3} \pi ).
- Confusing the volume formula for a sphere with other shapes (like cylinders or cones). Always remember the specific formula for the shape you are working with.
