Math Problem Statement
What is the volume of a sphere with a diameter of 27.3 in, rounded to the nearest tenth of a cubic inch?
Solution
To find the volume of a sphere, you can use the formula:
where is the radius of the sphere.
Given that the diameter of the sphere is 27.3 inches, the radius is half of the diameter:
Now, substitute the radius into the volume formula:
Calculating this:
Rounding to the nearest tenth:
So, the volume of the sphere is approximately 10,664.2 cubic inches.
Would you like further details or have any questions? Here are some related questions you might find interesting:
- How does the volume change if the diameter is doubled?
- What is the surface area of the same sphere?
- How do you derive the formula for the volume of a sphere?
- What is the volume of a hemisphere with the same radius?
- How does the volume of a sphere compare to the volume of a cylinder with the same height and diameter?
Tip: Remember that the volume of a sphere grows rapidly as the radius increases, since it’s proportional to the cube of the radius.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of a sphere
Formulas
Volume of a sphere: V = (4/3)πr^3
Theorems
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Suitable Grade Level
Grades 9-12