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Written Report-1 - For educational purposes

For educational purposes
Course

BSEd Filipino

58 Documents
Students shared 58 documents in this course
Academic year: 2021/2022
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Cebu Roosevelt Memorial College

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Name/s : JEAN A. CAMAY Subject : DIMENSIONAL ANALYSIS

VOLUME OF A SPHERE TITLE I. Content The volume of a sphere is the capacity it has. It is thvolume of a sphere is measured in cubic units, such as m3e space occupied by the sphere. The, cm3, in3, etc. The shape of the sphere is round and three-dimensional. It has three axedefines its shape. All the things like football and basketball ares as x-axis, y-axis and z-axis which examples of the sphere which have volume. The formula to find the volume of sphere is given by: Volume of sphere = 4/3 πr3 [Cubic units] Let us see how to derive the dimensional formula for the volume of a sphere. Derivation : The volume of a Sphere can be easily obtained using the integration method.

Assume that the volume of the sphere is made up of numearranged one over the other as shown in the figure givenrous thin circular disks which are above. The circular disks have continuously varying diameters which are placed with tany one of the disks. A thin disk has radius “r” and the thickness “dy” which is located at ahe centres collinearly. Now, choose distance of y from the x-axis. Thus, the volume can be the circle and its thickness dy. written as the product of the area of Also, the radius of the circular disc “r” can be expressed in terms of the vertical dimension (y) using the Pythagoras theorem.

Thus, the volume of the disc element, dV can be expressed by: dV =(πr2)dy dV =π (R2-y2) dy Thus, the total volume of the sphere can be given by:

Now, substitute the limits:

Simplify the above expression, we get:

Thus, the dimensional formula of volume of the sphere is

cubic units. How to Calculate Volume of Sphere? The volume of sphere is the space occupied within it. It can be calculated using the above formula, which we have already derived. To find the vsteps below: olume of a given sphere follow the

Check with the radius of the given sphere. If the diadivide it by 2, to get the radius meter of the sphere is known, then Find the cube of the radius r3Now multiply it with (4/3)π The final answer will be the volume of sphereLet us see some examples of calculating the volume of spheres of different dimensions.

Examples on Volume of Sphere Q: Find the volume of a sphere whose radius is 3 cm? Solution : Given: Radius, r = cm Volume of a sphere = 4/3 πr3 cubic units V = 4/3 x 3 x 33 V = 4/3 x 3 x 3 x 3 x 3

III. References byjus/maths/volume-of-sphere/

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Written Report-1 - For educational purposes

Course: BSEd Filipino

58 Documents
Students shared 58 documents in this course

University: Cebu Roosevelt Memorial College

Was this document helpful?
Name/s: JEAN A. CAMAY
Subject: DIMENSIONAL ANALYSIS
VOLUME OF A SPHERE
TITLE
I. Content
The volume of a sphere is the capacity it has. It is the space occupied by the sphere. The
volume of a sphere is measured in cubic units, such as m3, cm3, in3, etc. The shape of the
sphere is round and three-dimensional. It has three axes as x-axis, y-axis and z-axis which
defines its shape. All the things like football and basketball are examples of the sphere which
have volume.
The formula to find the volume of sphere is given by:
Volume of sphere = 4/3 πr3 [Cubic units]
Let us see how to derive the dimensional formula for the volume of a sphere.
Derivation:
The volume of a Sphere can be easily obtained using the integration method.
Assume that the volume of the sphere is made up of numerous thin circular disks which are
arranged one over the other as shown in the figure given above. The circular disks have
continuously varying diameters which are placed with the centres collinearly. Now, choose
any one of the disks. A thin disk has radius “r” and the thickness “dy” which is located at a
distance of y from the x-axis. Thus, the volume can be written as the product of the area of
the circle and its thickness dy.
Also, the radius of the circular disc “r” can be expressed in terms of the vertical dimension
(y) using the Pythagoras theorem.

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