A sphere is a three-dimensional geometric object which is perfectly in round shape. Mathematically, the sphere is a set of points equidistant from a single point. That common point of the sphere is called the center and distance between common point and any other point on the sphere is called the radius.
Sphere Calculator: Finding the sphere volume, circumference, radius, and surface area becomes quite easy with our online calculator. This article gives clear information regarding the simple formulas, step by step process to calculate the unknown measures of a sphere using the known details. Apart from this, you will also find the solved examples
User-friendly geometry tool Sphere Calculator computes the unknown parameters of a sphere effortlessly by taking the required details. You just need to provide known data values as input and press the calculate button to check the accurate output within no time.
Below mentioned are the basic and straightforward formulas to compute the sphere volume, circumference, and surface area by using the radius.
- Volume of a Sphere Formula:
- Volume V = (4/3)πr³
- Circumference of a Sphere Formula:
- Circumference C = 2πr
- Surface Area of a Sphere Formula:
- Surface Area A = 4πr²
This section gives the sphere formulas in terms of volume, circumference, and surface area.
- If sphere circumference is known, then
- Volume V = (C³ / 6π²)
- Radius r = C / 2π
- Surface Area A = C² / π
- If the surface area of a sphere is given, then
- Radius r = √(A / (4π))
- Volume V = (A3/2) / (6√π)
- Circumference C = √πA
- If sphere volume is given, then
- Circumference C = π2/3(6V)1/3
- Radius r = (3V / 4π)1/3
- Surface Area A = π1/3(6V)2/3
r is the sphere radius
V is the volume of a sphere
C is the sphere circumference
A is the sphere surface area
Steps to Solve Sphere Area, Circumference, Volume
The simple procedure to find the sphere area, radius, volume, surface area manually are given below. For the sake of your comfort, we have listed the detailed steps here. Use them and make your calculations much easier and quicker.
- Check out the sphere radius. Multiply the radius with 2π to find the circumference.
- Process 1:
- Note down the sphere volume from the question.
- Divide 3 times of volume by 4 times of π.
- Calculate the cube root of the result to check the radius.
- Find the sphere circumference.
- Divide the circumference by 2 times π.
- The obtained value is known as the radius of a sphere
- Process 3:
- Make a note of the sphere surface area from the question.
- Divide the surface area by 4 times of π.
- Apply square root to the result to get the radius.
- Get the sphere radius.
- Evaluate the cube of the radius.
- Multiply it with 4 times of π.
- Divide the value obtained from the above step by 3 to know the volume of a sphere.
Sphere Surface Area:
- Check out the radius of a sphere.
- Square the radius.
- Multiply it with 4 times of π to find the surface area.
Example Questions on Sphere
Example 1: Calculate the sphere volume, surface area, and circumference. If the sphere radius is 14 cm.
Sphere radius r = 14 cm
Sphere surface area formula is
Surface Area A = 4πr²
A = 4π * 14²
= 4π * 14 * 14 = 4π * 196
= 784 π = 784 * 3.14 = 2,461.76 cm²
Volume of a Sphere Formula is
Volume V = (4/3)πr³
V = (4/3)π * 14³
= (4/3)π * 14 * 14 * 14 = (4/3)π * 2744
= 10976π / 3
= 3,658.66π = 3,658.66 * 3.14 = 11,488.21 cm³
Circumference of a Sphere Formula is
Circumference C = 2πr
C = 2π * 14
= 28π = 28 * 3.14 = 87.92 cm
∴ Sphere volume is 11,488.21 cm³, surface area is 2,461.76 cm², circumference is 87.92 cm, and radius is 14 cm.
Example 2: Find the sphere radius, volume, circumference having a surface area of 616 cm².
Sphere surface area A = 616 cm²
Sphere Radius r = √(A / (4π))
r = √(616 / (4π))
= √(616 / (4 * 3.14)) = √(616 / 12.56)
= √49.04 = 7 cm
Volume of a sphere V = (A3/2) / (6√π)
V = 6163/2 / (6√π)
= 6163/2 / (6√3.14)
= 6163/2 / (6 * 1.772)
= 6163/2 / 10.632
= 1437.99 cm³
Circumference C = √(πA)
C = √(π * 616)
= √(3.14 * 616)
= √1,934.24 = 43.97 cm
∴ Sphere circumference is 43.97 cm, volume is 1437.99 cm³, radius is 7 cm, surface area is 616 cm².
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Frequently Asked Question's on Sphere Calculator
1. What are the properties of a Sphere?
The sphere is not a polyhedron
It is perfectly symmetrical.
It has constant mean curvature.
All points on the surface of a sphere are equidistant from the center.
It does not have a surface of centers.
2. How do you measure the volume of a sphere?
The formula to measure the volume of a sphere is volume = (4/3)π(radius)³. Find the radius and substitute it in the formula to get the volume easily.
3. How can you find the surface area of the sphere with the circumference?
The common parameter in the surface area and circumference is the radius. So, evaluate the radius from the circumference. C/ 2π is the radius. The surface area is circumferece² / π.
4. Is sphere a circle?
A circle is a two-dimensional shape. It has a perimeter and area. Whereas the sphere is a three-dimensional shape having surface area and volume.