A Glass Test Tube In A Chemistry Lab Holds A Sample Of Water. The Test Tube Is Cylindrical In Shape With A Rounded Hemisphere-shaped Bottom And A Diameter Of 2 Centimeters. The Water Fills The Test Tube To A Level 8 Centimeters Above Its Bottom, As

Introduction

A glass test tube in a chemistry lab holds a sample of water, which fills the test tube to a level 8 centimeters above its bottom. The test tube is cylindrical in shape with a rounded hemisphere-shaped bottom and a diameter of 2 centimeters. In this article, we will explore the geometry of the test tube and the water it contains, using mathematical concepts to understand the relationships between the different components.

The Cylindrical Test Tube

The test tube is a cylinder with a diameter of 2 centimeters. To find the radius of the test tube, we can divide the diameter by 2.

• Radius of the test tube: 2 cm / 2 = 1 cm

The test tube has a rounded hemisphere-shaped bottom, which means it is a hemisphere with a radius of 1 cm.

The Water in the Test Tube

The water fills the test tube to a level 8 centimeters above its bottom. To find the volume of the water, we need to find the volume of the cylinder that is occupied by the water.

• Height of the water: 8 cm
• Radius of the test tube: 1 cm

The volume of a cylinder is given by the formula:

V = πr^2h

where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius, and h is the height.

• Volume of the water: V = π(1)^2(8) = 3.14(1)(8) = 25.12 cm^3

The Hemisphere-Shaped Bottom

The test tube has a rounded hemisphere-shaped bottom, which means it is a hemisphere with a radius of 1 cm. The volume of a hemisphere is given by the formula:

V = (2/3)πr^3

where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius.

• Volume of the hemisphere-shaped bottom: V = (2/3)π(1)^3 = (2/3)(3.14)(1) = 2.09 cm^3

The Volume of the Water and the Hemisphere-Shaped Bottom

The volume of the water is 25.12 cm^3, and the volume of the hemisphere-shaped bottom is 2.09 cm^3. To find the volume of the water that is not occupied by the hemisphere-shaped bottom, we can subtract the volume of the hemisphere-shaped bottom from the volume of the water.

• Volume of the water not occupied by the hemisphere-shaped bottom: 25.12 cm^3 - 2.09 cm^3 = 23.03 cm^3

Conclusion

In this article, we explored the geometry of a cylindrical test tube and the water it contains. We used mathematical concepts to understand the relationships between the different components, including the radius of the test tube, the height of the water, and the volume of the water and the hemisphere-shaped bottom. By applying the formulas for the volume of a cylinder and a hemisphere, we were able to find the volume of the water and the hemisphere-shaped bottom, and to determine the volume of the water that is not occupied by the hemisphere-shaped bottom.

Mathematical Formulas

• Volume of a cylinder: V = πr^2h
• Volume of a hemisphere: V = (2/3)πr^3

References

• [1] "Geometry of a Cylinder". Math Open Reference.
• [2] "Geometry of a Hemisphere". Math Open Reference.

Further Reading

• "Mathematics for Chemistry". Oxford University Press.
• "Geometry and Trigonometry for Scientists and Engineers". Brooks Cole.

Glossary

• Cylinder: A three-dimensional shape with two parallel and circular bases connected by a curved lateral surface.
• Hemisphere: A three-dimensional shape that is half of a sphere.
• Radius: The distance from the center of a circle or sphere to the edge.
• Volume: The amount of space inside a three-dimensional shape.
  A Glass Test Tube in a Chemistry Lab: Q&A =============================================

Introduction

In our previous article, we explored the geometry of a cylindrical test tube and the water it contains. We used mathematical concepts to understand the relationships between the different components, including the radius of the test tube, the height of the water, and the volume of the water and the hemisphere-shaped bottom. In this article, we will answer some frequently asked questions about the test tube and the water it contains.

Q: What is the volume of the test tube?

A: The volume of the test tube is not directly relevant to the problem, as we are only interested in the volume of the water and the hemisphere-shaped bottom. However, if we assume that the test tube is a cylinder with a height of 10 cm (the height of the test tube plus the height of the water), we can use the formula for the volume of a cylinder to find the volume of the test tube.

• Volume of the test tube: V = πr^2h = π(1)^2(10) = 3.14(1)(10) = 31.4 cm^3

Q: What is the ratio of the volume of the water to the volume of the hemisphere-shaped bottom?

A: To find the ratio of the volume of the water to the volume of the hemisphere-shaped bottom, we can divide the volume of the water by the volume of the hemisphere-shaped bottom.

• Ratio of the volume of the water to the volume of the hemisphere-shaped bottom: 25.12 cm^3 / 2.09 cm^3 = 12.01

Q: What is the percentage of the volume of the water that is occupied by the hemisphere-shaped bottom?

A: To find the percentage of the volume of the water that is occupied by the hemisphere-shaped bottom, we can divide the volume of the hemisphere-shaped bottom by the volume of the water and multiply by 100.

• Percentage of the volume of the water occupied by the hemisphere-shaped bottom: (2.09 cm^3 / 25.12 cm^3) x 100 = 8.33%

Q: What is the volume of the water that is not occupied by the hemisphere-shaped bottom?

A: We already calculated this in our previous article: 23.03 cm^3.

Q: What is the ratio of the volume of the water not occupied by the hemisphere-shaped bottom to the volume of the hemisphere-shaped bottom?

A: To find the ratio of the volume of the water not occupied by the hemisphere-shaped bottom to the volume of the hemisphere-shaped bottom, we can divide the volume of the water not occupied by the hemisphere-shaped bottom by the volume of the hemisphere-shaped bottom.

• Ratio of the volume of the water not occupied by the hemisphere-shaped bottom to the volume of the hemisphere-shaped bottom: 23.03 cm^3 / 2.09 cm^3 = 11.01

Q: What is the percentage of the volume of the hemisphere-shaped bottom that is occupied by the water not occupied by the hemisphere-shaped bottom?

A: To find the percentage of the volume of the hemisphere-shaped bottom that is occupied by the water not occupied by the hemisphere-shaped bottom, we can divide the volume of the water not occupied by the hemisphere-shaped bottom by the volume of the hemisphere-shaped bottom and multiply by 100.

• Percentage of the volume of the hemisphere-shaped bottom occupied by the water not occupied by the hemisphere-shaped bottom: (23.03 cm^3 / 2.09 cm^3) x 100 = 110.1%

Conclusion

In this article, we answered some frequently asked questions about the test tube and the water it contains. We used mathematical concepts to understand the relationships between the different components, including the radius of the test tube, the height of the water, and the volume of the water and the hemisphere-shaped bottom. By applying the formulas for the volume of a cylinder and a hemisphere, we were able to find the volume of the water and the hemisphere-shaped bottom, and to determine the volume of the water that is not occupied by the hemisphere-shaped bottom.

Mathematical Formulas

• Volume of a cylinder: V = πr^2h
• Volume of a hemisphere: V = (2/3)πr^3

References

• [1] "Geometry of a Cylinder". Math Open Reference.
• [2] "Geometry of a Hemisphere". Math Open Reference.

Further Reading

• "Mathematics for Chemistry". Oxford University Press.
• "Geometry and Trigonometry for Scientists and Engineers". Brooks Cole.

Glossary

• Cylinder: A three-dimensional shape with two parallel and circular bases connected by a curved lateral surface.
• Hemisphere: A three-dimensional shape that is half of a sphere.
• Radius: The distance from the center of a circle or sphere to the edge.
• Volume: The amount of space inside a three-dimensional shape.