# Circular pool

The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?

Correct result:

x =  6102 hl

#### Solution:

r=10 \ \text{m} \ \\ t=10 \ \text{m} \ \\ h=2 \ \text{m} \ \\ a=t/2=10/2=5 \ \text{m} \ \\ \ \\ α=2 \cdot \ \arcsin ( \dfrac{ a }{ r } )=2 \cdot \ \arcsin ( \dfrac{ 5 }{ 10 } ) \doteq 1.0472 \ \text{rad} \ \\ α_{2}=α \rightarrow ^\circ =α \cdot \ \dfrac{ 180 }{ \pi } ^\circ =1.0472 \cdot \ \dfrac{ 180 }{ \pi } ^\circ =60 ^\circ ^\circ \ \\ \ \\ S_{1}=\pi \cdot \ r^2 \cdot \ \dfrac{ 2 \pi - α }{ 2 \pi }=3.1416 \cdot \ 10^2 \cdot \ \dfrac{ 2 \cdot \ 3.1416 - 1.0472 }{ 2 \cdot \ 3.1416 } \doteq 261.7994 \ \text{m}^2 \ \\ \ \\ b=\sqrt{ r^2-a^2 }=\sqrt{ 10^2-5^2 }=5 \ \sqrt{ 3 } \ \text{m} \doteq 8.6603 \ \text{m} \ \\ \ \\ S_{2}=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 5 \cdot \ 8.6603 }{ 2 } \doteq 21.6506 \ \text{m}^2 \ \\ \ \\ S=S_{1} + 2 \cdot \ S_{2}=261.7994 + 2 \cdot \ 21.6506 \doteq 305.1007 \ \text{m}^2 \ \\ \ \\ V=h \cdot \ S=2 \cdot \ 305.1007 \doteq 610.2013 \ \text{m}^3 \ \\ \ \\ x=V \rightarrow \ \text{hl}=V \cdot \ 10 \ \ \text{hl}=610.2013 \cdot \ 10 \ \ \text{hl}=6102 \ \text{hl}

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The text passage describes a math problem involving the calculation of the volume of a circular pool with a specific shape and dimensions. It provides a detailed solution to the problem, including the necessary formulas and steps to find the volume in hectoliters.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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system
# Circular pool

The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?

Correct result:

x =  6102 hl

#### Solution:

r=10 \ \text{m} \ \\ t=10 \ \text{m} \ \\ h=2 \ \text{m} \ \\ a=t/2=10/2=5 \ \text{m} \ \\ \ \\ α=2 \cdot \ \arcsin ( \dfrac{ a }{ r } )=2 \cdot \ \arcsin ( \dfrac{ 5 }{ 10 } ) \doteq 1.0472 \ \text{rad} \ \\ α_{2}=α \rightarrow ^\circ =α \cdot \ \dfrac{ 180 }{ \pi } ^\circ =1.0472 \cdot \ \dfrac{ 180 }{ \pi } ^\circ =60 ^\circ ^\circ \ \\ \ \\ S_{1}=\pi \cdot \ r^2 \cdot \ \dfrac{ 2 \pi - α }{ 2 \pi }=3.1416 \cdot \ 10^2 \cdot \ \dfrac{ 2 \cdot \ 3.1416 - 1.0472 }{ 2 \cdot \ 3.1416 } \doteq 261.7994 \ \text{m}^2 \ \\ \ \\ b=\sqrt{ r^2-a^2 }=\sqrt{ 10^2-5^2 }=5 \ \sqrt{ 3 } \ \text{m} \doteq 8.6603 \ \text{m} \ \\ \ \\ S_{2}=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 5 \cdot \ 8.6603 }{ 2 } \doteq 21.6506 \ \text{m}^2 \ \\ \ \\ S=S_{1} + 2 \cdot \ S_{2}=261.7994 + 2 \cdot \ 21.6506 \doteq 305.1007 \ \text{m}^2 \ \\ \ \\ V=h \cdot \ S=2 \cdot \ 305.1007 \doteq 610.2013 \ \text{m}^3 \ \\ \ \\ x=V \rightarrow \ \text{hl}=V \cdot \ 10 \ \ \text{hl}=610.2013 \cdot \ 10 \ \ \text{hl}=6102 \ \text{hl}

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Tips to related online calculators
Do you know the volume and unit volume, and want to convert volume units?

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Pascal's law
Please calculate according to Pascal's law. Krupp's machines were known for their large size. In 1861, a blacksmith's steam hydraulic press was put into operation in Essen. What was the cross-sectional area of the larger piston if a compressive force of 1
• Gears
The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the rear wheel of the bike turns if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm?
• Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
• Winch drum
Originally an empty winch drum with a diameter of 20 cm and a width of 30 cm on the rescue car, he started winding a rope with a thickness of 1 cm beautifully from edge to edge. The winch stopped after 80 turns. It remains to spin 3.54m of rope (without h
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• Metal tube
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• The pot
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• Velocipedes
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• Cylinder height
Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
• Collect rain water
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• Height as diameter of base
The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
• Special watch
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user
The text passage describes a math problem involving the calculation of the volume of a circular pool with a specific shape and dimensions. It provides a detailed solution to the problem, including the necessary formulas and steps to find the volume in hectoliters.

TYPE: SINGLE_QUESTION_WITH_ANSWER