Understanding the Basics of a Sphere

Oct 13, 2025 by windailys.com 12 views

**What is the Volume of a Sphere with a Diameter of 2.2 ft, Rounded to the Nearest Tenth of a Cubic Foot?**

Understanding the Basics of a Sphere

A sphere is a three-dimensional shape that is perfectly round and has no corners or edges. It is a continuous curved surface that is symmetrical about its center. The volume of a sphere is a measure of the amount of space inside the sphere.

Calculating the Volume of a Sphere

The formula to calculate the volume of a sphere is:

V = (4/3) * π * r^3

Where V is the volume of the sphere, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sphere.

Converting Diameter to Radius

To calculate the volume of the sphere, we need to know the radius of the sphere. The radius is half the diameter of the sphere. Given that the diameter of the sphere is 2.2 ft, we can calculate the radius as follows:

r = diameter / 2 r = 2.2 ft / 2 r = 1.1 ft

Calculating the Volume of the Sphere

Now that we have the radius of the sphere, we can calculate the volume of the sphere using the formula:

V = (4/3) * π * r^3 V = (4/3) * 3.14159 * (1.1 ft)^3 V = (4/3) * 3.14159 * 1.331 V = 5.265 ft^3

Rounding the Volume to the Nearest Tenth of a Cubic Foot

The calculated volume of the sphere is 5.265 ft^3. To round this value to the nearest tenth of a cubic foot, we need to look at the hundredth place, which is 6. Since 6 is greater than or equal to 5, we round up the tenth place to 5.3.

Conclusion

In conclusion, the volume of a sphere with a diameter of 2.2 ft, rounded to the nearest tenth of a cubic foot, is 5.3 ft^3.

Frequently Asked Questions

Q: What is the formula to calculate the volume of a sphere?

A: The formula to calculate the volume of a sphere is V = (4/3) * π * r^3.

Q: What is the radius of a sphere with a diameter of 2.2 ft?

A: The radius of a sphere with a diameter of 2.2 ft is 1.1 ft.

Q: How do I round a decimal value to the nearest tenth?

A: To round a decimal value to the nearest tenth, look at the hundredth place. If the hundredth place is 5 or greater, round up the tenth place. If the hundredth place is 4 or less, round down the tenth place.

Q: What is the volume of a sphere with a diameter of 2.2 ft?

A: The volume of a sphere with a diameter of 2.2 ft is 5.265 ft^3.

Q: How do I calculate the volume of a sphere with a given diameter?

A: To calculate the volume of a sphere with a given diameter, first convert the diameter to radius by dividing by 2. Then, use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: What is the significance of the value π in the formula to calculate the volume of a sphere?

A: The value π is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159.

Q: Can I use a calculator to calculate the volume of a sphere?

A: Yes, you can use a calculator to calculate the volume of a sphere. Simply enter the radius of the sphere and use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: How do I convert a diameter to a radius?

A: To convert a diameter to a radius, simply divide the diameter by 2.

Q: What is the relationship between the diameter and the radius of a sphere?

A: The radius of a sphere is half the diameter of the sphere.

Q: Can I use the formula to calculate the volume of a sphere to calculate the volume of a cylinder?

A: No, the formula to calculate the volume of a sphere is specific to spheres and cannot be used to calculate the volume of a cylinder.

Q: What is the significance of the value 4/3 in the formula to calculate the volume of a sphere?

A: The value 4/3 is a constant that represents the ratio of the volume of a sphere to the cube of its radius.

Q: Can I use a spreadsheet to calculate the volume of a sphere?

A: Yes, you can use a spreadsheet to calculate the volume of a sphere. Simply enter the radius of the sphere and use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: How do I calculate the volume of a sphere with a given radius?

A: To calculate the volume of a sphere with a given radius, use the formula V = (4/3) * π * r^3.

Q: What is the relationship between the volume of a sphere and its radius?

A: The volume of a sphere is proportional to the cube of its radius.

Q: Can I use the formula to calculate the volume of a sphere to calculate the volume of a cone?

A: No, the formula to calculate the volume of a sphere is specific to spheres and cannot be used to calculate the volume of a cone.

Q: What is the significance of the value π in the formula to calculate the volume of a sphere in terms of geometry?

A: The value π represents the ratio of a circle's circumference to its diameter, which is a fundamental property of geometry.

Q: Can I use a calculator to calculate the volume of a sphere with a given diameter?

A: Yes, you can use a calculator to calculate the volume of a sphere with a given diameter. Simply enter the diameter and use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: How do I calculate the volume of a sphere with a given diameter and a given height?

A: To calculate the volume of a sphere with a given diameter and a given height, first convert the diameter to radius by dividing by 2. Then, use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: What is the relationship between the volume of a sphere and its diameter?

A: The volume of a sphere is proportional to the cube of its diameter.

Q: Can I use the formula to calculate the volume of a sphere to calculate the volume of a rectangular prism?

A: No, the formula to calculate the volume of a sphere is specific to spheres and cannot be used to calculate the volume of a rectangular prism.

Q: What is the significance of the value 4/3 in the formula to calculate the volume of a sphere in terms of mathematics?

A: The value 4/3 is a constant that represents the ratio of the volume of a sphere to the cube of its radius, which is a fundamental property of mathematics.

Q: Can I use a spreadsheet to calculate the volume of a sphere with a given radius?

A: Yes, you can use a spreadsheet to calculate the volume of a sphere with a given radius. Simply enter the radius and use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: How do I calculate the volume of a sphere with a given diameter and a given radius?

A: To calculate the volume of a sphere with a given diameter and a given radius, first convert the diameter to radius by dividing by 2. Then, use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: What is the relationship between the volume of a sphere and its radius in terms of geometry?

A: The volume of a sphere is proportional to the cube of its radius, which is a fundamental property of geometry.

Q: Can I use the formula to calculate the volume of a sphere to calculate the volume of a pyramid?

A: No, the formula to calculate the volume of a sphere is specific to spheres and cannot be used to calculate the volume of a pyramid.

Q: What is the significance of the value π in the formula to calculate the volume of a sphere in terms of mathematics?

A: The value π represents the ratio of a circle's circumference to its diameter, which is a fundamental property of mathematics.

Q: Can I use a calculator to calculate the volume of a sphere with a given radius and a given height?

A: Yes, you can use a calculator to calculate the volume of a sphere with a given radius and a given height. Simply enter the radius and use the formula V = (4/3) * π * r^3 to calculate the volume.

Q: How do I calculate the volume of a sphere with a given diameter and a given height and a given radius?

A: To calculate the volume of a sphere with a given diameter and a given height and a given radius, first convert the diameter to radius by dividing by 2. Then, use the formula V = (4/3) * π * r^3 to calculate the volume.