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Solids

 

Solids are three-dimensional figures of various two-dimensional shapes. Unlike two-dimensional shapes, which have only area, three-dimensional solids have both surface area and volume. The inside space of a solid represents its volume. In contrast, the outer area is its surface area.

We can find the internal area of solids as well. For example, when we need to paint our room, we need to do it internally and externally. In such cases, we need to find both inside and outside areas of the walls.

A solid shape will have a face, vertices and edges. The face is the flat surface of any solid outside it. Edges are the lines where two or more sides meet. Vertices are the corners where two or sides meet in a solid.

Solid Shapes Faces Edges Vertices
Sphere 1 0 0
Cylinder 2 2 0
Cone 1 1 1
Cube 6 12 8
Cuboid 6 12 8
Triangular Prism 5 9 6
Pentagonal Prism 7 15 10
Hexagonal Prism 8 18 12
Square Pyramid 5 8 5
Triangular Pyramid 4 6 6
Pentagonal Pyramid 6 10 6
Hexagonal Pyramid 7 12 7

There are various solid shapes having different volumes and areas. Some of these solid shapes which are used in our day to day lives are described below.

Shape Image Property Surface area Volume
Cube IMAGE 2 It has 6 faces, 8 vertices and 12 edges.
It is a three-dimensional shape of a square. All the sides of the cube are equal.
6a²
Cuboid IMAGE 3 A cuboid is a polyhedron having 6 faces, 12 edges and 8 vertices. It is the three-dimensional figure of a rectangle. The faces of a cuboid are parallel. Total Surface area = 2 [(l x b) + (b x h) + (l x h)]
Lateral surface area = 2 h (l + b)
l x b x h
Sphere IMAGE 4 It has no edges or vertices. It has only one surface. It is shaped like a ball and is perfectly symmetrical. All points on the surface are at the same distance from the center. 4πr² (4/3) πr³
Prism IMAGE 5 It has identical ends (polygonal) and flat faces, and possesses the same cross-section all along its length. 2 × (BA) + P × H BA × H
Cone IMAGE 6 It has a circular or oval base with an apex (a pointed top). It has one curved side. A cone is a vertical triangle that is rotated about a fixed axis of symmetry. πr (r + s)
where, s = slant height
1/3 πr² h
Cylinder IMAGE 7 It has a flat base and top. Its one side is curved. The bases are always congruent and parallel. It is a three-dimensional object with two identical ends; either circular or oval. 2πr (r + h) πr² h
Pyramid IMAGE 8 A pyramid is a polyhedron with a polygon base and an apex with straight lines. They can be classified into regular and oblique pyramids based on their apex alignment with the center of the base. BA + 1/2 × P × (SH)
Where, BA = base area, SH = slant height, and P = perimeter
1/3 BA²
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