Math Problem Statement
What is the maximum volume of water
that can be filled in such a bottle? (Use π = 22/7, Formula for the volume of a cylinder = πr²h)
А. 14,142.86 cm³
В. 31,821.43 cm³
С. 56,571.43 cm³
D. 127,285.71 ст³
Solution
To find the maximum volume of water that can be filled in the bottle, we need to calculate the volume of the cylinder using the given formula:
where:
- is the radius of the cylinder
- is the height of the cylinder
From the image:
- The diameter of the bottle is , so the radius
- The height
Let's calculate the volume.The maximum volume of water that can be filled in the bottle is approximately 14,142.86 cm³.
The correct answer is A. 14,142.86 cm³.
Would you like a detailed breakdown of this calculation or have any further questions?
Related Questions:
- What would be the volume if the diameter was doubled?
- How would the volume change if the height was increased to 60 cm?
- How does the choice of π value (3.14 vs. 22/7) affect the volume calculation?
- What is the surface area of this cylindrical bottle?
- How do you calculate the volume of a cone?
Tip:
Remember that the volume formula for a cylinder relies heavily on the square of the radius; small changes in the radius result in larger changes in the volume.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume Calculation
Formulas
Volume of a cylinder = πr²h
Theorems
Cylindrical Volume Calculation
Suitable Grade Level
Grades 6-8