In the above shown diagram,
r is the radius
C is the base circumference
V is the volume
A is the curved surface area
B is the base surface area
K is the total surface area
π is pi whose value is equal to 3.14159
The total surface area of any sphere that has a radius is 4 * π * r * r
The sphere is basically a three dimensional circle that can be also said as the circle that is present in space. The best example for differentiating a sphere with a circle is a ring and a ball. A ring is a circle and a ball is a sphere. Circles and sphere both are round and both of them are measured with a radius. But a circle is mainly drawn on a plane and the sphere is drawn as three dimensional. Circle is basically a closed figure that can be drawn with possible constant length that is taken from a fixed point centre. This particular fixed point centre is called a circle and the total distance that is drawn on the circle is known as the radius of the circle. The line that passes through centre of the circle from one end to another end is commonly known as diameter and half of the diameter is known as radius if the circle.
The surface area of the sphere is 4 * π * r * r
A sphere if cut in to halves, each part is known as hemisphere. For example, if the earth is divided in to halves, each part of the earth will a hemisphere. Earth has two spheres, southern hemisphere as well as northern hemisphere. In case of each hemisphere, there are curved surface area and there is total surface area. The total area that is present in the outer portion is constituted as CSA (Curved Surface Area) of the hemisphere. The total surface are (K) of a hemisphere is mainly obtained by addition of the total curved surface area with the total area of the upper circle of hemisphere. There are two types of hemisphere that are available; solid hemisphere and hollow hemisphere.
The formula for the area of hemisphere is stated below:
Curved surface of a hemisphere: The sphere is cut in to halves. So the curved surface area will be the half of the area of the sphere.
The formula can be written as 2 * π * r * r
The total surface area of hemisphere is calculated as the total surface area of the hemisphere. For calculating the total surface area of a hemisphere, the base of the hemisphere is to be considered. The total surface area in the hemisphere is equal to
Total surface area = the total curved surface area + the area of base circle
= 2 * π * r * r + π * r * r
As hemisphere is also available as hollow hemisphere. The area of the hollow hemisphere is the total area of the external hemisphere – area of the internal hemisphere.
To find out the volume of the hemisphere, Archimedes principle is used. According to the Archimedes principle, if a solid figure is immersed in some container and it is filled with water, the total volume of water in that container that comes out from that container is considered as the total volume of that solid figure.
When a spherical figure is inserted in a cylindrical figure that is filled with water, the total amount of water that that comes out from the cylinder is the total volume of the sphere.
In the figure above, the spherical body marked in red is inside the cylindrical container. The radius of the sphere is equal to the radius of the base of the cylinder. The diameter of the sphere is also equal to the diameter of the sphere. The spherical body touches the top as well as bottom of the container.
The total volume of the spherical body is mostly assumed is the 2/3rd of cylindrical container. This can be stated as Vsphere = 2/3 V cylinder or can be written as 2/3 * π * r * r * h.
h = 2 * r
So, it can be written as 2/3 * π * r * r (2 * r) = 4/3 * π * r * r * r
The volume of the hemisphere can be written as the half of the total volume of that particular sphere. The volume of that hemisphere is equal to ½ * 4/3 * π * r * r * r
That is it can be written as 2/3 * π * r * r * r
Example of calculating the volume of sphere is
Let the diameter of the earth be x, then the radius of the earth will be x/2
So, volume of the Earth be 4/3 * π * x/2 * x/2 * x/2.
The radius of the moon = 2 * diameter of the moon = ½ * ¼ * x = x/8
So, the volume of the moon is 4/3 * π * x/8 * x/8 * x/8.
For the above question, the diameter of the hemisphere is given as 14 cm
So, for calculating the Curved Surface Area, the formula for the hemisphere will be 2 * π * r * r
So, from the given data, the diameter of the hemisphere is 14 cm. So, the radius of the hemisphere will be 7 cm.
So putting the value of the radius in the curved surface area formula, we get
2 * π * r * r
= 2 * 3.14 * 7 * 7
= 307.876 cm2
So, from the above calculated example, the curved surface area of the hemisphere of 14 com diameter will be 307.876 cm2.
The CSA of the sphere will be 2 * 307.876 cm2 = 615.752 cm2
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