Today, i will teach you how to calculate a round object.This round object is known as "Sphere" which 3 dimensional parts.Orange and grapes are examples of spherical objects.Spherical objects have the shape of a sphere,even though they may not be perfect spheres like onions etc.We say that,Earth is also a spherical object. A globe is sued to represent the shape of the earth.This mathematics has a formula
4
-----------ㄫr³
3
Football, table tennis balls, the moon and the sun are all spherical objects.
Hemisphere
Each of the two equal halves of a sphere is called a hemisphere is a circle,whose center is the center of the sphere.
Radius of a Sphere
The distance from the center of a sphere to any point on the sphere is a constant, called the slant of a sphere (R).
Volume of a Sphere of a Radius R
We say that, the volume of an object is the amount of space occupied by the object
Example 1
Calculate the volume of a sphere of radius 7cm ( Take ㄫ = 22/7)
Solution
4
-----------ㄫr³
3
4 22
= ----------- x --------- x 7³
3 7
88 x 49
= -----------------
3
4312
= ---------------
3
1
= 1 437 ----------cm³ Volume
3
Example 2
Find the volume of a solid hemisphere of radius 7/2 cm (Take pie = 22/7)
Solution
Radius of solid hemisphere , R = 7/2 cm , ㄫ = 22/7
Volume of solid hemisphere =
2
1 4
-------- ( --------- ㄫR³ )
2 22 7
= ---------- x ----------- x (------- )³
3 7 2
44 x 49
= ---------------------
3 x 8
539
=----------------
6
5
= 89 ------- cm³ Volume
6
Remember that 1 part of hemisphere is half, that while i begin with 1/2.
Example 3
Find the radius of a sphere whose volume is 36ㄫ cm³.
Solution
Volume of a sphere = 36ㄫ
36ㄫ x 3
= ------------------ = 27
4 ㄫ
R = ₃√ 27 = 3cm
Now let solve the one in real life.
Example 4
A solid metal spherical ball of radius 3cm is put inside a plastic box of dimensions 8cm by 7cm by 10cm.If the box is filled completely with water,find the volune of the water in the box.
Solution
Volume of box = (L X B X H) cm³
= 8 x 7 x 10
= 560 cm³
4
Volume of ball = ---------- ㄫR³
3
4 22
= --------- x ---------- 3³
3 7
792
= ------------
7
1
=113 --------
7
Volume of water in the box = ( volume of box) - ( Volume of ball)
1
= ( 560 cm³ ) - ( 113 -------- cm³ )
7
6
= 446 ------------ cm³
7
The reason why i started the volume of box is that , box is bigger that ball.That means, it is only the biggest number can subtract smallest number.
I hope you understand this topic, if you have any question, please put it in the comments box.
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