Introduction
Let us draw a circle and a sphere on a piece of paper. What do we find? Both the shapes are the same because of their round format. Thus, many of us get confused in understanding them. Then what is the difference between a circle and a sphere? The basic sphere and circle difference is that the circle is 2-Dimensional, and a sphere is 3-Dimensional. Deriving from the basic difference, we can get another difference that is one can compute the area of a circle, but for a sphere, we have to find its volume.
Circle
A circle is considered a type of line. A circular line consists of a set of points with a property that all the points present in that line are from a uniform distance from a fixed point on a plane. It consists of a closed-loop that divides plains into inner and outer sections. The various properties of a circle are center, circumference, tangent, and chord. Radius is connected to its center through the lines, and "r" depicts the length of the radius of that particular circular line. Ellipse is a special case of a circle with a set of points with a constant sum of the distance between the two fixed points in a plane. These two fixed points are known as focus and center, which are the same in the case of a circle. In the inner circle, one can find three sets of points that are not present in the same direction, which defines a triangle's edges. Some examples of the circle are disc, clock, etc.
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Sphere
Unlike a circle, a sphere is a three-dimensional figure. All the points of a sphere are equidistant from the center at any of the axes. You can calculate the volume, surface area, and radius of the sphere easily.
The line connecting the distant edge points is known as the diameter of the sphere. There is no circumference present in the sphere. There are small circles and hemispheres present in the sphere. Some popular examples of spheres include marble, football, and water droplets.
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Types of Spheres
Solid Sphere - Solid object, which is in the form of a sphere, is known as a solid sphere. A solid sphere is filled with the same material from which it is made up of.
Hollow Sphere- When a solid sphere is cut from the middle and a big solid that is taken out of it, leaving a spherical shell behind, is called a hollow sphere.
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Difference between Circle and Sphere
Because of the round shape of both circle and sphere, people find both similar to each other. But in reality, both are quite different from each other. Let us illustrate some major differences between circle and sphere.
Solved Example
How would you calculate the surface area of a ball whose radius is 5 cm?
Ans: Firstly, we would like to disclose that the ball is a sphere. The radius of the ball is given as 5 cm.
Surface area of sphere = 4 πr2
Therefore, the surface area of the ball = 4π(5)2
= 4 x π x 25
= 100 π sq.cm.
FAQs on Difference Between Circle and Sphere for JEE Main 2024
1. Mention different types of spheres?
As such, there are plenty of diverse spheres around you in mathematics, but the most popular ones stand out to be solid and hollow spheres.
Solid Sphere: The sphere in solid form and object is referred to as the solid sphere. It is filled with the same material from which it was made initially.
Hollow Sphere: The next popular kind of sphere is a hollow sphere. When the solid portion is taken out from the middle of the sphere leaving a hollow and empty space behind is known as a hollow sphere.
2. Are both circles and spheres the same?
The answer is NO. Many students feel the circle and sphere to be the same because of the round shape they possess. But they have many differences between both, which are enough to differentiate both from each other. A circle is a two-dimensional figure, whereas a sphere is a three-dimensional figure. Circle refers to the closed curved line and sphere is a round object in space. Each point from the circle is of equal distance, but in the sphere, the distance varies.
3. What do you Mean by Hemisphere? How to Find Out the Volume of a Hemisphere?
In the word hemisphere, Hemi means half. So, half of a sphere is known as a hemisphere. A sphere is a set of three-dimensional points for the center equidistant with all the points. Our earth comprises two hemispheres, the northern and the southern hemispheres which are exactly divided into two shapes from the earth's midpoint.
Hemisphere is the half of a sphere.
As we know that the volume of the sphere is \[\frac{4}{3} \pi r^{3}\]
The volume of hemisphere =\[\frac{1}{2} \times \frac{4}{3} \pi r^{3} = \frac{2}{3} \pi r^{3}\]
Where r is the radius of the hemisphere.
4. How to Derive the Formula of a Sphere?
As we know that the volume of a cylinder = πr²h
Volume of cylinder = volume of sphere + volume of cone
Volume of cylinder = 3 × volume of cone
πr²h = 3 × volume of cone
\[\frac{1}{3} \pi r^{2}h\] = volume of cone
Volume of sphere = \[\frac{1}{3} \pi r^{2}h + \frac{1}{3} \pi r^{2}h \]
The height of a cone = diameter of the sphere =2r
So, replace h =2r
The volume of the sphere will be = \[2 \times (\frac{2}{3}) \pi r^{3}\]
Therefore, the volume of the sphere is \[\frac{4}{3} \pi r^{3}\]
