Math Problem Statement
the volume of a sphere is 36pie ft3. what is the radius is the sphere
Solution
The volume of a sphere is given by the formula:
Where:
- is the volume of the sphere.
- is the radius.
- is Pi, approximately 3.14159.
You're given that the volume of the sphere is , so we can set up the equation:
Now, divide both sides by to simplify:
Next, multiply both sides by 3 to eliminate the fraction:
Now, divide both sides by 4:
Finally, take the cube root of both sides to find :
So, the radius of the sphere is .
Would you like more details or have any questions? Here are some related questions to expand your understanding:
- What is the formula for the surface area of a sphere?
- How does the volume of a sphere change if its radius is doubled?
- What is the relationship between the volume of a sphere and a cube with the same radius?
- Can you derive the volume formula of a sphere using calculus?
- What is the difference in volume between two spheres with radii 3 ft and 6 ft?
Tip: When dealing with volume formulas, always make sure to work with consistent units for accurate calculations!
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume
Spheres
Formulas
Volume of a sphere: V = (4/3)πr³
Theorems
Formula for the volume of a sphere
Suitable Grade Level
Grades 8-10