How to Calculate the Diameter of a Sphere from its Curved Surface Area

In this tutorial, we will walk you through the steps of finding the diameter of a sphere given its curved surface area. This is an essential skill for anyone working with three-dimensional geometry and will help you solve various real-world problems efficiently.

Understanding the Formula

The formula for the curved surface area of a sphere is given by:

A 4πr2

In this formula, A represents the curved surface area, and r denotes the radius of the sphere. The value of π (pi) is typically taken as 22/7 or approximately 3.14159.

Given Data

In this specific scenario, the curved surface area (A) is given as 394.24.

A 394.24

Step-by-Step Calculation

Start with the given formula:

A 4πr2

Substitute the given value of the curved surface area:

394.24 4πr2

Isolate r2 by dividing both sides by (4π):

r2 394.24 / (4π)

Solve for r2 using the value of π as 22/7:

r2 394.24 / (4 × 22/7)

r2 394.24 / (88/7)

r2 394.24 × 7/88

r2 ≈ 31.36

Calculate the radius (r) by taking the square root of r2:

r √31.36 ≈ 5.6

Finally, calculate the diameter (d), which is twice the radius:

d 2r

d 2 × 5.6 11.2

Conclusion

The diameter of the sphere is 11.2 units. This process can be applied to any problem where the curved surface area of a sphere is known, and the diameter is needed.

Frequently Asked Questions (FAQs)

Q: What is the curved surface area of a sphere?

A: The curved surface area (cSA) of a sphere is the area of the outer surface, excluding the top and bottom, and is calculated using the formula 4πr2, where r is the radius of the sphere.

Q: How do you find the radius given the curved surface area?

A: To find the radius (r), you need to rearrange the formula for the curved surface area: r √(A / 4π), where A is the given curved surface area.

Q: What is the diameter of a sphere?

A: The diameter of a sphere is twice the radius (d 2r). It is the length of a line segment that passes through the center of the sphere and whose endpoints lie on the sphere's surface.

Additional Resources

For more detailed information on the properties of spheres and other geometric shapes, you can refer to the following resources:

Math is Fun - Sphere Khan Academy - Sphere Volume and Surface Area