A is a perfect symmetrical shape that is three-dimensional with all points on its equidistant from its center. Finding the of a sphere can be crucial in many scientific equations, including those used in physics, engineering, and astronomy. In this article, we will discuss how to find the radius of a sphere using different methods.

Method 1: Using the Volume Formula

The of a sphere is given by the formula:

V = (4/3)πr³

Where V is the volume of the sphere and r is its radius.

If we know the volume of a sphere, we can find its radius by rearranging the formula as:

r = (3V/4π)^(1/3)

For example, if we have a sphere with a volume of 100 cubic centimeters, we can find its radius as follows:

r = (3 * 100 / 4π)^(1/3)

r = 2.65 centimeters

Method 2: Using the Surface Area Formula

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

A = 4πr²

Where A is the surface area of the sphere and r is its radius.

If we know the surface area of a sphere, we can find its radius by rearranging the formula as:

r = √(A/4π)

For example, if we have a sphere with a surface area of 50 square centimeters, we can find its radius as follows:

r = √(50 / 4π)

r = 1.59 centimeters

Method 3: Using the Circumference Formula

The circumference of a sphere is given by the formula:

C = 2πr

Where C is the circumference of the sphere and r is its radius.

If we know the circumference of a sphere, we can find its radius by rearranging the formula as:

r = C / 2π

For example, if we have a sphere with a circumference of 20 centimeters, we can find its radius as follows:

r = 20 / 2π

r = 3.18 centimeters

Method 4: Using the Diameter

The diameter of a sphere is the distance across its widest part, passing through its center. If we know the diameter of a sphere, we can find its radius by dividing the diameter by 2 (since the radius is half the diameter).

For example, if we have a sphere with a diameter of 12 centimeters, we can find its radius as follows:

r = 12 / 2

r = 6 centimeters

Conclusion

There are different methods to find the radius of a sphere. Depending on the available information, we can use the volume formula, the surface area formula, the circumference formula, or the diameter. These formulas are useful in solving different scientific equations, as well as in practical applications in engineering and architecture. With this information, we can now find the radius of any sphere given its volume, surface area, circumference, or diameter.

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