Three dimensions can be measured, length, width, and height, for any object that you can see or touch. There are certain dimensions of our home that we live in. The rectangular display screen/Monitor you’re looking at has the width and breadth of its own length.
For every threedimensional geometrical structure, surface area and volume are measured.
Surface Area & Volume
Surface area refers to the measurement of the space taken up by a flat twodimensional surface. This measurement is expressed in terms of square units. For threedimensional objects, the surface area represents the space occupied by their outer surfaces. Similar to the flat surface area, it is also measured in square units.
In general, there are two types of surface area
Total surface area is the combined measurement of the base(s) and the curved portion of an object. It represents the sum of the object's surface coverage. In cases where the object's shape includes both a curved surface and a base, the total surface area is calculated by summing up the measurements of these two areas.
Curved surface area pertains to the measurement of only the curved portion of a shape, excluding any base(s). This aspect is also referred to as the lateral surface area, particularly for shapes like a cylinder.
Cube is a solid shape having 6 equal square faces of length l.
Lateral surface area of a cube =4l^{2}
Total surface area of cube=6l ^{2}
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Cuboid is a solid shape having 6 rectangular faces at a right angle with length l, breadth b and height h.
Lateral surface area of a cuboid= 2h(l+b)
Total surface area of a cuboid= 2(lb+bh+lh)
If we fold a rectangular sheet with one side as its axis then it forms a cylinder. It is the curved surface of the cylinder. And if this curved surface is covered by two parallel circular bases then it forms a right circular cylinder. For a cylinder of height h and with base radius r.
Curved surface area of a Right circular cylinder=2πrh
Total surface area of a Right circular cylinder=2πr^{2}+2πrh=2πr(r+h)
If a right circular cylinder is hollow from inside then it has a different curved surface.
Curved surface area of a Right circular cylinder=2πh(R+r)
Total surface area of a Right circular cylinder=2πh(R+r)+2π(R^{2} −r^{2)}
If we revolve a rightangled triangle about one of its sides by taking other as its axis then the solid shape formed is known as a Right Circular Cone.
Curved surface area of a Right Circular Cone = πrl=πrh^{2}+r^{2}
Total surface area of a Right Circular Cone= πr^{2}+πrl=πr(r+l)
A sphere is a solid shape which is completely round like a ball. It has the same curved and total surface area.
Curved or Lateral surface area of a Sphere=4πr^{2}
Total surface area of a Sphere=4πr^{2}
If we cut the sphere in two parts then it is said to be a hemisphere.
Curved or Lateral surface area of a Hemisphere=2πr^{2}
Total surface area of a Hemisphere=3πr^{2}
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l=length, b= breadth, h=height
Side of cube = a
r = Radius of Cylinder
h = Height of Cylinder
h= height of cone
r = radius of cone
l = slant height of cone = (h^{2}+r^{2})
r= radius
Radius = r
115 videos478 docs129 tests

1. What is the formula for calculating the surface area of a cylinder? 
2. How do you calculate the volume of a sphere? 
3. Can you explain how to find the surface area of a cone? 
4. What is the formula for finding the volume of a rectangular prism? 
5. How do you calculate the surface area of a cube? 
115 videos478 docs129 tests


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