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Sphere Formula
Everything you need to know about the sphere formula is provided below. Please proceed to read the whole document carefully to understand the topic completely.
A sphere is a fully symmetrical three-dimensional circular shaped object. The radius of the square is the line that links the centre to the boundary. On the surface of a sphere, you may discover a point that is equidistant from any other point.
The diameter of the sphere is the longest straight line that runs through the centre of the sphere. It is twice the radius of the sphere in length.
Formulas for Sphere
The sphere diameter formula, sphere surface area formula, and sphere volume formula are the three major formulae for a sphere.
Diameter of Sphere
A sphere’s diameter is defined as a straight line travelling through its centre and touching two points on either side of its surface. A sphere’s diameter is always two times its radius. If the sphere’s radius is ‘r,’ the diameter may be calculated using the formula:
2 x r = D
Circumference of a Sphere
A sphere’s circumference is equal to two times its radius. The formula for calculating the circumference of a sphere and a circle is the same:
C = 2 π r
π is a constant with the value of 3.14 or 22/7. As a result, a sphere’s circumference may be calculated as 6.28 times or 44/7 times its radius.
Total surface area of Sphere
Because there are no lateral surfaces on a sphere, its total surface area is the same as its curved surface area. The formula for calculating a sphere’s surface area is stated mathematically as:
TSA = 4πr2
In the equation above,
The total surface area of a sphere is known as TSA. π is a constant with the value of 3.14 or 22/7 as its value.
The value of ‘r’ represents the radius of the provided sphere.
As a result, the formula for calculating a sphere’s surface area is 4 times, 12.56 times, or 88/7 times the radius square of the sphere.
Volume of a Sphere
Deriving the volume of a sphere is the same as finding the total space available within the surface of the sphere. The mathematical formula for deriving the volume of a sphere is given as:
V = 4/3r3
In the above equation,
‘V’ is the volume of the sphere
Π is a constant and its value is equal to 3.14 or 22/7.
‘r’ represents the value of the radius of the given sphere.
So, the formula for the deriving volume of a sphere can be stated as 4π/3 times or 4.19 times, or 88/21 times the cube of the radius of the sphere whose volume is to be determined.
Solved Examples
1. Calculate the diameter and the circumference of a sphere whose radius is 10 cm.
Solution:
Given: Radius of the sphere = 10 cm
The diameter of the sphere is calculated as:
D = 2 x r
D = 2 x 10
D = 20 cm
Circumference of the sphere is found by the formula
C = 2 x π x r
C = 2 x (22/7) x10
C = 62.8571 cm
Therefore, the diameter and circumference of the sphere are 20cm and 62.8571 cm, respectively.
2. Find the total surface area and the volume of a sphere whose radius is 7cm.
Solution:
Given: Radius of the sphere = 7 cm
The formula for the deriving surface area of a sphere is:
A = 4πr2
A = 4 x (22/7) x (7 )2
A = 4 x (22/7) x 7 x 7
A = 4 x 22 x 7
A = 616 cm2
The volume of a sphere is found using the formula:
V = (4/3) π r3
V = (4/3) x (22/7) x (7 )3
V = 1437.33 cc
Therefore, the volume and total surface area of a sphere of radius 7 cm are 1437.33 cc and 616 cm2, respectively.
3. The volume of a sphere is found to be 729 cc. Find its radius.
Solution:
Given: Volume of the sphere = 729 cc
The formula for deriving the volume of a sphere is.
V = 4/3πr3
729 = (4/3) (22/7) r3
729 = (88/21) r3
r3 = (729 x 21) / 88
r3 = 173.97
r = ∛173.97
r = 5.58 cm
Therefore, the radius of the sphere is 5.58 cm
