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Diameter Formula is used to measure the diameter of a circle. By using the diameter formula, the distance between the two edges of the circle can be calculated. The diameter of a circle is two times the length of a radius of the circle. A circle contains numerous diameters. In a circle, the diameter can be defined as a line that passes through the middle point of the circle and joins two points laid on the edge of the circle.
There are various objects presented in circular shapes such as clock, ball, bangle, etc. In geometry, these are explained as circles. Within the circle, there is one point that is referred to as the centre and the distance from one point to another within the circle is known as diameter.
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Key Terms: Diameter, Centre, Radius, Line Segment, Distance, Circle
What is a Diameter?
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Diameter can be defined as a straight line that passes through the centre of the circle. A circle contains an infinite number of diameters. Also, each diameter within a circle is placed with equal lengths. The length of a diameter is equal to twice the length of radius of a circle. Diameter is also known as the longest chord of the circle. Some other important terms related to a circle are:
- Centre: It is a point in the middle of a circle from where the distance to the boundary of the circle is constant.
- Circumference: Circumference of Circle is defined as a set of points placed at an identical distance around the middle place of the circle.
- Radius: It is explained as the distance that connects two points from the centre to the circumference.
- Tangent: Tangent to a Circle may be defined as a line that touches the circle boundary at exactly one point. It is always perpendicular to the radius of the circle.
- Chord: Any line segment drawn from one point of a circle to another point is known as chord.
- Area: Area of circle is described as the number of spaces within the circle.
Parts of a Circle
Diameter Formula
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There are various formulas used to solve problems of diameter. Below are some important formulas given.
- Formula 1: 2 × Radius
The radius of a circle is defined as a straight line that is elongated from the midpoint of a circle to the exterior of it. On the other side, the diameter can be classified as the distance between the two points placed on the border of a circle. A diameter is explained as twice the radius of the circle. However, the relation between diameter and radius is explicated in this formula.
- Formula 2: Circumference ÷ π
Circumference can be defined as the perimeter of a circle. The diameter formula can be derived from Circumference. To get the diameter, the circumference must be divided by π. In this formula, C is referred to as circumference whereas D is considered as diameter and π are considered as constant.
- Formula 3: 2√Area/π
In mathematics, this is considered the most important constant. The area of a circle is pi times of the radius squared and the area unit can be explained as a square unit. Pi is defined as the ratio of circumference to diameter of a circle.
Diameter Formulas
How to Calculate Diameter?
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There are various ways by which the diameter of a circle is calculated. Some of the important ways are given below:
- Diameter can be calculated by using radius. By doubling the radius, the diameter will be created. For instance, when the radius of the circle is 6, the diameter of that circle will be 6 x 2 = 12 cm.
- Diameter can be calculated by using circumference. To get the diameter, the circumference will be divided by π. The exact value will be calculated with the help of a calculator. For example, when the circumference of a circle is 25cm/π or 7.95 cm.
- Calculations of diameter are done by the area of a circle. To get the diameter, the output will be divided by π and after getting the square roots for radius, multiply it by the number 2. For instance, when the area of a circle is 12cm² and this is divisible by π, then the square root by using the formula will be:
When 12/3.14 = √3.82,
Diameter of circle = 1.95 x 2 = 3.90 cm.
Things to Remember
- In the matter of radius, diameter is used either as line segment or as length.
- An arc is considered a semicircle in a situation where its last point is the end of a diameter.
- The formula of diameter is calculated by doubling a circle's radius.
- The complete arc of a circle is measured as 360° whereas the arc of a semicircle is 180°.
- In a circle, a diameter makes two equal semicircles. But the centre of diameter is the midpoint of the circle.
- The area and perimeter or circumference is found in a circle. But it doesn't have any volume.
- A sector is formed by converging two radii. However, a sector is defined as a region that lies between two radii.
Sample Questions
Ques. The area of a circle is 300 square cm. What is the diameter of a circle? (3 marks)
Ans. Given that the area of circle = 300 square cm
We know that,
D = 2 × √(A/π
Substituting the given values in above equation, we get:
D = 2 × (√300π
= 2 × (√3003.14
= 2 × 9.77cm
= 19.54 cm
Hence, the diameter of a circle is 19.54 cm.
Ques. The radius of a circle is 24 inches long. Calculate the diameter of a circle. (2 marks)
Ans. Given that the radius of the circle = 24 inches
We know that,
D = 2 × Radius
Substituting the given values in above equation, we get:
D = 2 × 24 inches = 48 inches
So, the diameter of the circle is 48 inches.
Ques. The circumference of the circle is 8π units. What will be the diameter of a circle? (2 marks)
Ans. Given that the circumference of circle = 8π units
We know that,
D = Circumference/π
Also, Circumference/π = 8π units,
Therefore, the diameter of the circle is 8 units.
Ques. The diameter of the circle is 12 units. What is the value of radius? (2 marks)
Ans. Given that the diameter of the circle = 12 units
We know that,
D = 2 × Radius
Substituting the given values in above equation, we get:
Diameter = 2 × Radius
Radius = D ÷ 2
Radius = 12 ÷ 2 = 6 units
So, the radius of the circle will be 6 units.
Ques. The circumference of the tire of a car is 24 inches. What is the diameter and nearest travel distance after 3 full cycling of a tire? (3 marks)
Ans. Given that the circumference of the tire of a car = 24 inches
We know that,
C = πd
Substituting the given values in above equation, we get:
24 = πd
Diameter = 24/3.14 = 7.64 inches
Therefore, the diameter is 7.64 inches
The nearest distance after 3 rotations is 24 x 3= 72 inches
However, 12 inches = 1ft
So, 72/12 = 6 feet
Ques. The circumference of the circle is 32 cm. Calculate the diameter of a circle. (3 marks)
Ans. Given that the circumference of the circle = 32 cm
We know that,
C = πd
Substituting the given values in above equation, we get:
32 = (3.14) d
Following this, both sides will be divided by 3.14.
After leaving D, 32 will be divided by 3.14. And the solution will be 10.19 cm.
The radius is 5.09 cm (10.19/2)
Ques. The radius of a circle is 15 cm. What is the value of the diameter of the circle? (2 marks)
Ans. Given that the radius of the circle = 24 inches
We know that,
D = 2 × Radius
Substituting the given values in above equation, we get:
D = 15 × 2
R = 30 cm.
Ques. A circle is 113.04 square inches. What is the radius of a circle? (2 marks)
Ans. Given that the area of circle = 113.04 square inches
We know that,
A = πr2
Substituting the given values in above equation, we get:
113.04 = (3.14)r2
113.04/3.14 = r2
36 = r2
After removing the square root from both the side, the outcome will be 6 = r
Therefore, the radius of the circle is 6 inches.
Ques. The area of a circle is 379.94 cm2. Find out the diameter of a circle. (3 marks)
Ans. Given that the area of circle = 379.94 cm2
We know that,
A = πr2
Substituting the given values in above equation, we get:
379.94 = (3.14)r2
379.94/3.14 = r2
121 = r2
After taking the square root from both the side, the solution will be 11 = r
Then, D = 2r
D = 2×11 = 22 cm
Hence the diameter of the circle = 22 cm.
Ques. The volume of a spare is identical in terms of the figure to the area of its surface. What is the diameter of the sphere? (3 marks)
Ans. The radius of the sphere is R
The volume of a sphere is equal to the surface area of the sphere
Hence, 4/3 πr3 = 4 πr3
r = 3 cm
So, the diameter of the sphere is 2r = 2 x 3 = 6 cm.
Ques. Both the spare and a right circular cylinder having the same radius are alike in terms of volumes. Find out the maximum percentage of the height of the cylinder. (3 marks)
Ans. By using formula, 4/3 πr3 = πr3h
4/3 r = h = r = 3/4 h
As radius = ¾ x height of the cylinder
So, the diameter of the cylinder is 2 x r = 2 x 3/4 h = 3/2 h
Height increases = (3/2 - 1)h = 1/2 h
Hence, the percentage = 2/h x 100 = 50
Ques. What is the formula of surface area of the circle? (2 marks)
Ans. Both the area of a circle and the surface area of a circle are the same. When the 3D form of a surface occupies an area, then that area is called a surface area. The shape of the circle is 2 dimensional. When the radius, diameter and circumference of a circle are present then the area of the surface is found. It is represented by square units.
Ques. How is the derivation of the circle area defined? (3 marks)
Ans. First of all, a circle is parted into 12 sectors that are the same.
Divide 2 same halves of a sector. After that, a total of 13 sectors will be present in that circle.
Then arrange all the sectors in a rectangular shape. The height along with the width will be the same.
Circumference = 2 × π × radius
Width = Half the Circumference = π × radius
Hence, the area of the rectangle will be (π × radius) × (radius) = π × radius²
Ques. How is the sector and perimeter of a circle explained with the real-life example? (2 marks)
Ans. The sector is derived from the centre of a circle. As an example, a slice of a pizza can be given. All the slices are sectors. When it has 6 equal portions or slices, then each portion is called a sector. Here, the radius of the pie will be 7 inches.
A perimeter with a 2-dimensional shape can be defined as the total length of the side of it. When it comes to a real-life example, a garden with fencing can be given as an example of a perimeter.
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