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The area and volume of different 2D and 3D shapes are very important in mathematics (mensuration). It and every shape which is created in 2 dimensions (which has x-axis and y-axis) have area.
And all the other shapes which have all the other shapes on which both x-axis, y-axis, and z-axis have volumes, theses shapes made in the third dimension are known as solids and the amount of space they occupy are known as Solid. (These are three-dimensional shapes)
Area, Volume (Menstruation)
Area, Volume (Mensuration) are important parts of mathematics where the amount of space occupied by any type of flat surface (2D shape) is called its area.
And the capacity occupied by any 3D object is considered as its volume, it is calculated in cubical units.
Curved Surface Area of Hemisphere
A sphere when cut into two equal halves, then its half is called a hemisphere.
The Curved Surface Area of the Hemisphere: The outer area of the surface of the hemisphere is known as its curved surface area.
Since we know that the hemisphere is the half of a sphere if the radius is given its curved surface area can be written as:
Curved surface area of a hemisphere = 1/2 (Curved surface area of a sphere) = 1/2 (4 π r2) = 2 π r2
Let’s take an example for a better understanding.
Example: Find the Curved Surface area of the hemisphere which has a radius of 5 cm.
Solution: Radius= 5 cm (Given)
So, the curved surface area of the hemisphere will be:
2*(22/7) *5*5 #CSA= 2πr2
157.14 square cm.
Total Surface of a Cylinder formula
The Total Surface area of a Cylinder is the total space that is covered by any plane surface of its base and its curved surface. It has two main points which are a curved surface area and two flat surface areas.
The total surface area is presented in square units, the radius of the base of the cylinder is ‘r’ and the height of the cylinder is ‘h’, the surface area of a cylinder is
Total Surface Area, T = 2πr (r + h)
For better understanding let’s take an example.
Example: Find the Total surface area of the cylindrical container which has a height of 12 cm, and a radius is 14 cm.
Solution: Radius= 14 cm; (Given)
Height= 12 cm; (Given)
Then the Total surface area of the cylinder will be:
2*(22/7) *14*(14+12) # TSA = 2πr (h + r)
2,288 square cm.
Surface Area and Volume of all formulae
The Surface area and Volume of all shapes are very important in mathematics, the amount of area which is covered by the surface of something is referred to as its Surface area and Volume is the amount of space that is covered by any type of 3D object. The perimeter is the distance around any object.
All the 2D and 3D formulas are given below:
Conclusion
The Topic Area, Volume (Mensuration) falls under mathematics. Above has been discussed the mensuration formulas of the 2D and 3D shapes. The FAQs section attempts to address the most probable queries that might arise. The FAQs section provides additional information which will aid a better understanding of the topic.
