Understanding the Formula for the Volume of a Hemisphere

Oct 13, 2025 by miodeya.com 127 views

**What is the Volume of a Hemisphere with a Diameter of 60.9 Inches?**

A hemisphere is half of a sphere, and its volume can be calculated using a specific formula. In this article, we will explore the concept of the volume of a hemisphere and provide a step-by-step solution to calculate the volume of a hemisphere with a diameter of 60.9 inches.

Understanding the Formula for the Volume of a Hemisphere

The formula for the volume of a hemisphere is:

V = (2/3)πr³

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

Calculating the Radius of the Hemisphere

To calculate the volume of the hemisphere, we need to find the radius of the hemisphere. The radius is half of the diameter, so we can calculate it as follows:

r = diameter/2 r = 60.9/2 r = 30.45 inches

Calculating the Volume of the Hemisphere

Now that we have the radius, we can plug it into the formula to calculate the volume of the hemisphere:

V = (2/3)πr³ V = (2/3) × 3.14159 × (30.45)³ V = (2/3) × 3.14159 × 298,535.51 V = 198,764.19 cubic inches

Rounding the Volume to the Nearest Tenth of a Cubic Inch

The problem asks us to round the volume to the nearest tenth of a cubic inch. To do this, we need to round 198,764.19 to the nearest tenth, which is 198,764.2 cubic inches.

Conclusion

In this article, we have explored the concept of the volume of a hemisphere and provided a step-by-step solution to calculate the volume of a hemisphere with a diameter of 60.9 inches. We have also rounded the volume to the nearest tenth of a cubic inch.

Frequently Asked Questions

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

A: The formula for the volume of a hemisphere is V = (2/3)πr³.

Q: How do I calculate the radius of a hemisphere?

A: To calculate the radius of a hemisphere, you need to divide the diameter by 2.

Q: What is the volume of a hemisphere with a diameter of 60.9 inches?

A: The volume of a hemisphere with a diameter of 60.9 inches is approximately 198,764.2 cubic inches.

Q: How do I round a volume to the nearest tenth of a cubic inch?

A: To round a volume to the nearest tenth of a cubic inch, you need to look at the hundredth place and decide whether to round up or down.

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

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

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

A: No, you cannot use the formula for the volume of a sphere to calculate the volume of a hemisphere. You need to use the formula for the volume of a hemisphere, which is V = (2/3)πr³.

Q: What is the significance of the constant π in the formula for the volume of a hemisphere?

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

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

A: Yes, you can use a calculator to calculate the volume of a hemisphere. However, make sure to use the correct formula and enter the correct values.

Q: What is the unit of measurement for the volume of a hemisphere?

A: The unit of measurement for the volume of a hemisphere is cubic inches.

Q: Can I calculate the volume of a hemisphere with a diameter of 60.9 inches using a calculator?

A: Yes, you can calculate the volume of a hemisphere with a diameter of 60.9 inches using a calculator. However, make sure to use the correct formula and enter the correct values.

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

A: The volume of a hemisphere is half of the volume of a sphere.

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

A: No, you cannot use the formula for the volume of a hemisphere to calculate the volume of a sphere. You need to use the formula for the volume of a sphere, which is V = (4/3)πr³.

Q: What is the significance of the constant 2/3 in the formula for the volume of a hemisphere?

A: The constant 2/3 is a mathematical constant that represents the ratio of the volume of a hemisphere to the volume of a sphere.

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. However, make sure to use the correct formula and enter the correct values.

Q: What is the unit of measurement for the volume of a sphere?

A: The unit of measurement for the volume of a sphere is cubic inches.

Q: Can I calculate the volume of a sphere with a radius of 30.45 inches using a calculator?

A: Yes, you can calculate the volume of a sphere with a radius of 30.45 inches using a calculator. However, make sure to use the correct formula and enter the correct values.

Q: What is the relationship between the volume of a hemisphere and the volume of a cylinder?

A: The volume of a hemisphere is not directly related to the volume of a cylinder. However, you can use the formula for the volume of a hemisphere to calculate the volume of a hemisphere, and then use the formula for the volume of a cylinder to calculate the volume of a cylinder.

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

A: No, you cannot use the formula for the volume of a hemisphere to calculate the volume of a cylinder. You need to use the formula for the volume of a cylinder, which is V = πr²h.

Q: What is the significance of the constant π in the formula for the volume of a cylinder?

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

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

A: Yes, you can use a calculator to calculate the volume of a cylinder. However, make sure to use the correct formula and enter the correct values.

Q: What is the unit of measurement for the volume of a cylinder?

A: The unit of measurement for the volume of a cylinder is cubic inches.

Q: Can I calculate the volume of a cylinder with a radius of 30.45 inches and a height of 60.9 inches using a calculator?

A: Yes, you can calculate the volume of a cylinder with a radius of 30.45 inches and a height of 60.9 inches using a calculator. However, make sure to use the correct formula and enter the correct values.

Q: What is the relationship between the volume of a hemisphere and the volume of a cone?

A: The volume of a hemisphere is not directly related to the volume of a cone. However, you can use the formula for the volume of a hemisphere to calculate the volume of a hemisphere, and then use the formula for the volume of a cone to calculate the volume of a cone.

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

A: No, you cannot use the formula for the volume of a hemisphere to calculate the volume of a cone. You need to use the formula for the volume of a cone, which is V = (1/3)πr²h.

Q: What is the significance of the constant π in the formula for the volume of a cone?

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

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

A: Yes, you can use a calculator to calculate the volume of a cone. However, make sure to use the correct formula and enter the correct values.

Q: What is the unit of measurement for the volume of a cone?

A: The unit of measurement for the volume of a cone is cubic inches.

Q: Can I calculate the volume of a cone with a radius of 30.45 inches and a height of 60.9 inches using a calculator?

A: Yes, you can calculate the volume of a cone with a radius of 30.45 inches and a height of 60.9 inches using a calculator. However, make sure to use the correct formula and enter the correct values.

Q: What is the relationship between the volume of a hemisphere and the volume of a pyramid?

A: The volume of a hemisphere is not directly related to the volume of a pyramid. However, you can use the formula for the volume of a hemisphere to calculate the volume of a hemisphere, and then use the formula for the volume of a pyramid to calculate the volume of a pyramid.

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

A: No, you cannot use the formula for the volume of a hemisphere to calculate the volume