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

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)

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:

Volume of a cylinder=πr2h\text{Volume of a cylinder} = \pi r^2 h

where:

  • π=227\pi = \frac{22}{7}
  • rr is the radius of the cylinder
  • hh is the height of the cylinder

From the image:

  • The diameter of the bottle is 20cm20 \, \text{cm}, so the radius r=202=10cmr = \frac{20}{2} = 10 \, \text{cm}
  • The height h=45cmh = 45 \, \text{cm}

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:

  1. What would be the volume if the diameter was doubled?
  2. How would the volume change if the height was increased to 60 cm?
  3. How does the choice of π value (3.14 vs. 22/7) affect the volume calculation?
  4. What is the surface area of this cylindrical bottle?
  5. 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