Math Problem Statement
What is the volume of this sphere? the radius is 36
Use 𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
Solution
The volume of a sphere is given by the formula:
where is the radius of the sphere and is approximately 3.14.
Given that , we can plug this into the formula:
First, calculate :
Now, plug this value back into the formula:
Calculate the result step by step:
So, the volume of the sphere is approximately 195,330.56 cubic units.
Do you have any questions or want further details?
Here are 5 related questions to expand on this:
- How does the formula for a sphere's volume compare to that of a cylinder?
- How would the volume change if the radius was doubled?
- Can you derive the volume formula for a sphere using calculus?
- How would using a more accurate value for affect the result?
- What would be the surface area of this sphere?
Tip: Always calculate exponents before multiplying by other terms in a formula for best accuracy.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of a Sphere
Formulas
V = (4/3) π r^3
Theorems
-
Suitable Grade Level
Grades 8-10