The Volume Of A Tube 785cm3 If The Tube Height Is 10cm And P = 3.14 Then The Surface Area Of ​​the Tube Is

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Introduction

In mathematics, particularly in geometry, understanding the properties of three-dimensional objects is crucial for solving various problems. One such object is a tube, which can be thought of as a cylinder with a circular base. In this article, we will delve into the world of tubes and explore the relationship between its volume, height, and surface area. We will use the given information - a tube with a volume of 785cm3, a height of 10cm, and the value of pi (p) as 3.14 - to calculate the surface area of the tube.

Understanding the Volume of a Tube

The volume of a tube, also known as a cylinder, is given by the formula:

V = πr2h

where V is the volume, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the tube.

Given that the volume of the tube is 785cm3 and the height is 10cm, we can use the formula to find the radius of the tube.

785 = πr2(10)

Calculating the Radius of the Tube

To find the radius of the tube, we need to rearrange the formula to isolate r.

r2 = 785 / (π(10)) r2 = 785 / (3.14(10)) r2 = 785 / 31.4 r2 = 25 r = √25 r = 5cm

Understanding the Surface Area of a Tube

The surface area of a tube, also known as a cylinder, is given by the formula:

A = 2πrh + 2πr2

where A is the surface area, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the tube.

Calculating the Surface Area of the Tube

Now that we have found the radius of the tube, we can use the formula to find the surface area.

A = 2πrh + 2πr2 A = 2(3.14)(5)(10) + 2(3.14)(5)2 A = 314 + 78.5 A = 392.5cm2

Conclusion

In this article, we have used the given information - a tube with a volume of 785cm3, a height of 10cm, and the value of pi (p) as 3.14 - to calculate the surface area of the tube. We have first found the radius of the tube using the formula for the volume of a tube, and then used the formula for the surface area of a tube to find the surface area. The surface area of the tube is 392.5cm2.

Frequently Asked Questions

  • What is the formula for the volume of a tube? The formula for the volume of a tube is V = πr2h.
  • What is the formula for the surface area of a tube? The formula for the surface area of a tube is A = 2πrh + 2πr2.
  • How do I find the radius of a tube? To find the radius of a tube, you can use the formula for the volume of a tube and rearrange it to isolate r.
  • How do I find the surface area of a tube? To find the surface area of a tube, you can use the formula for the surface area of a tube and plug in the values for r, h, and π.

References

Further Reading

Introduction

In our previous article, we explored the relationship between the volume, height, and surface area of a tube. We used the given information - a tube with a volume of 785cm3, a height of 10cm, and the value of pi (p) as 3.14 - to calculate the surface area of the tube. In this article, we will answer some frequently asked questions related to the volume and surface area of a tube.

Q&A

Q: What is the formula for the volume of a tube?

A: The formula for the volume of a tube is V = πr2h, where V is the volume, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the tube.

Q: What is the formula for the surface area of a tube?

A: The formula for the surface area of a tube is A = 2πrh + 2πr2, where A is the surface area, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the tube.

Q: How do I find the radius of a tube?

A: To find the radius of a tube, you can use the formula for the volume of a tube and rearrange it to isolate r. The formula is r2 = V / (πh), and then take the square root of both sides to find the radius.

Q: How do I find the surface area of a tube?

A: To find the surface area of a tube, you can use the formula for the surface area of a tube and plug in the values for r, h, and π. The formula is A = 2πrh + 2πr2.

Q: What is the relationship between the volume and surface area of a tube?

A: The volume and surface area of a tube are related in that the surface area is proportional to the square of the radius, while the volume is proportional to the cube of the radius. This means that as the radius of the tube increases, the surface area increases more rapidly than the volume.

Q: How do I calculate the volume of a tube with a given surface area?

A: To calculate the volume of a tube with a given surface area, you can use the formula for the surface area of a tube and rearrange it to isolate V. The formula is V = (A - 2πr2) / (2πr), where A is the surface area, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the tube.

Q: What is the significance of the value of pi (p) in the formulas for the volume and surface area of a tube?

A: The value of pi (p) is a mathematical constant that is approximately equal to 3.14. It is used in the formulas for the volume and surface area of a tube to account for the circular shape of the base of the tube.

Conclusion

In this article, we have answered some frequently asked questions related to the volume and surface area of a tube. We have provided the formulas for the volume and surface area of a tube, as well as explanations for how to use them to find the radius and surface area of a tube. We have also discussed the relationship between the volume and surface area of a tube, and how to calculate the volume of a tube with a given surface area.

Frequently Asked Questions

  • What is the formula for the volume of a tube?
  • What is the formula for the surface area of a tube?
  • How do I find the radius of a tube?
  • How do I find the surface area of a tube?
  • What is the relationship between the volume and surface area of a tube?
  • How do I calculate the volume of a tube with a given surface area?
  • What is the significance of the value of pi (p) in the formulas for the volume and surface area of a tube?

References

Further Reading