Content Writer
The main difference between a circle and a sphere is that a circle is a two-dimensional space, while a sphere is a three-dimensional figure. A circle has all points at the same distance from its centre along a plane.
- In a sphere, all the points are equidistant from the centre at any of the axes.
- The circle has two foci that meet at the same point, with the line segment bent in a circular form.
- You might not be able to draw an actual sphere on a piece of paper.
- The line joining the centre to the boundary is called the radius of the sphere.
- The line joining from the centre of a circle to any point on the circumference of the surface is called the radius of the circle.
- Diameter divide the segments of circle into equal halves.
Definition of Circle and Sphere
[Click Here for Sample Questions]
The definition of circle and sphere are as follows:
Circle
A circle corresponds to a circular line such that all the points on the line are equidistant from a particular point on a plane. The line forms a closed loop that divides the plane into two parts: the inner section and the outer section.
Different Parts of a Circle
A circle consists of several parts: centre, circumference, chord, tangent, and radius.
- Centre of the circle is the point from which all the points on the circular line are equidistant.
- The circumference of a circle is the total length of the circular line, also known as the boundary of the circle.
- The chord of a circle corresponds to a line segment joining any two points on the circumference of the circle.
- Tangent corresponds to a line that touches the circle at a single point.
- The radius of a circle is the line segment connecting the centre of the circle to any point on its circumference.
- It is denoted by the symbol “r.”
Sphere
A sphere corresponds to a three-dimensional geometrical object which is an analogue to a two dimensional circle. It can be defined as a set of points which are all equidistant from a given point in the space.
Different Parts of a Sphere
Several parts of a sphere: centre, Radius, chord, diameter and poles
- Centre of a circle is the point that lies inside the circle and is equidistant from all the points on the surface of the sphere.
- Radius of a sphere is the line segment joining the centre of the sphere to a point on the surface of the sphere.
- Chord is the line segment joining any two points on the surface.
- Diameter of a sphere is the chord that passes through the centre of the sphere.
- The points that lie on the surface of the sphere and pass through the axis of the sphere are termed as Poles.
Read More:-
| Chapter Related Concepts | ||
|---|---|---|
| Section Formula | Area of Rectangle | Perimeter of a Circle |
| Surface Area and Volume Force | Semi-Circle | Frequency Polygons |
What is the difference between Circle and Sphere?
[Click Here for Sample Questions]
The difference between circle and sphere are as follows:
| PROPERTIES | CIRCLE | SPHERE |
|---|---|---|
| Definition | A circle corresponds to a circular line such that all the points on the line are equidistant from a particular point on a plane. The line forms a closed loop that divides the plane into two parts: inner section and outer section. | A sphere corresponds to a three-dimensional geometrical object which is an analogue to a two dimensional circle. It can be defined as a set of points which are all equidistant from a given point in the three dimensional space. |
| Dimension | Two-dimensional | Three-dimensional |
| Determination | Area is determined | Area or Volume is determined |
| Area/Surface Area | Area = πr2 | Surface Area = 4πr2 |
| Volume | A circle has no volume as it is a two dimensional figura. | Volume of sphere = 4/3πr3 |
| Diameter | 2r, where r is the radius of the circle. | 2r, where r is the radius of the sphere. |
| Circumference | 2πr, where r is the radius of the circle. | Sphere does not have a circumference. |
| Standard Equation | The standard equation of a circle is (x-a)2 + (y-b)2 = r2, where (a, b) is the centre of the circle and r is the radius of the circle. | The standard equation of a sphere is (x-a)2 + (y-b)2 + (z-c)2 = r2, where (a, b, c) is the centre of the sphere and r is the radius of the circle. |
| Consideration | Considered as a figure. | Considered as an object. |
| Examples | Discs, Clocks, Ring, etc. | Ball, Earth, Oranges, etc. |
Difference between Circle and Sphere
Things To Remember
[Click Here for Sample Questions]
- A circle corresponds to a circular line such that all the points on the line are equidistant from a particular point on a plane.
- The line forms a closed loop that divides the plane into two parts: the inner section and the outer section.
- A sphere corresponds to a three-dimensional geometrical object which is an analogue to a two dimensional circle.
- A hollow sphere is a sphere that consists of a space or a cavity inside itself.
- The standard equation of a circle is (x-a)2 + (y-b)2 = r2, where (a, b) is the centre of the circle and r is the radius of the circle.
- The standard equation of a sphere is (x-a)2 + (y-b)2 + (z-c)2 = r2, where (a, b, c) is the centre of the sphere and r is the radius of the circle.
Read More:-
Sample Questions
Ques: Calculate the circumference of a ring whose radius is 2m? (2 marks)
Ans: Given value : radius of the circle = 2 metre
Formula for circumference of a circle = 2πr
Putting the required values
Circumference of the ring = 2 x π x 2
= 2 x 3.14 x 2
= 12.56 m
Ques: Find the area of a circle with radius 3 cm? (2 marks)
Ans: Given value : radius of the circle = 3 cm
Formula for the area of given circle = πr2
Putting the required values
Area of the circle = πr2
= 3.14 x 3 x 3
= 28.26 cm2
Ques: Find the area of a circle if the given circumference is 44 m? (2 marks)
Ans: Given circumference = 44 m
Circumference of the circle = 2πr
44 = 2πr
r = 44 / 2π
r = (44 x 7) / (22 x 2)
r = 7 m
Here, the value of the radius is 7m.
Area of the circle =\( πr^2 \)
= (22 / 7) x 7 x 7 m2
= 154 m2
Ques: Find the volume of a sphere with radius 21 m? (2 marks)
Ans: Given radius of the sphere = 21 m
Volume of the sphere = 4/3\(πr^3\)
= (4/3) x (22/7) x 21 x 21 x 21 r3
= 4 x 22 x 21 x 21 r3
= 38,808 m3
Ques: Calculate the surface area of the sphere with radius 5 cm? (2 marks)
Ans: GIven radius of the sphere = 5 cm
Surface area of the sphere = 4\(πr^2\)
= 4 x 3.14 x 5 x 5 cm2
= 314 cm2
Ques: Write the general equation of circle and sphere? (2 marks)
Ans: The standard equation of a circle is (x - a)2 + (y - b)2 = r2
The standard equation of a sphere is (x - a)2 + (y - b)2 + (z - c)2 = r2
Ques: What is a hemisphere? And its volume formula? (1 mark)
Ans: Half of a sphere is known as the hemisphere. The volume of a hemisphere is 4/6πr3 .
Ques: Answer the following: (A) Explain the circumference of a circle and a sphere?
(B) What is an Ellipse? (2 marks)
Ans: (A) The circumference of a circle is the total length of the circular line also known as the boundary of the circle. On the other hand the circumference of a sphere does not exist.
(B) Ellipse corresponds to a special case of a circle with a set of points with a constant sum of the distance between the two fixed points (also known as focus) in a plane.
Ques: Find the circumference of the sector with a radius of 6 cm and an angle of 36°. π = 3.14? (2 marks)
Ans. The formula for finding the length of a sector is 2r + 2Πr X θ /360
2 x 6 + 2 x 3.14 x 6 x 36 /360
= 12 + 3.768
= 15.768 cm.
Ques: Find the perimeter of the circle if its radius is 5cm? (2 marks)
Ans: We know that,
The perimeter of circle = 2πr2
= 2×3.14×10
= 62.8cm
Ques: Find the volume of the sphere having a radius of 4 inches? (2 marks)
Ans: Given,
r = 9 inches
As we know, the volume of sphere, V = (4/3)πr3
Thus, volume of sphere, V = (4/3)πr3 = ((4/3) × π × 93) in3
V = 3052.08 in3
For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates
Check-Out:
Comments