In Geometry, the shape or the figure that has three (even higher) dimensions, are well-known as solids or three-dimensional shapes. The research of the properties, volume and also surface area the three-dimensional forms is referred to as Solid Geometry. Let us go ahead and focus more on the research of geometrical solids.

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Geometric Shapes

The geometrical figures classified based upon the dimensions room as follows:

Zero dimensional shape – A point.One dimensional shape – A line that has a length as its dimension.Two-dimensional shapes – A number that has actually length and breadth as 2 dimensions. For instance – square, triangle, rectangle, parallelogram, trapezoid, rhombus, quadrilateral, polygon, circle etc.Three-dimensional forms – an object with length, breadth and also height as 3 dimensions. For instance – cube, cuboid, cone, cylinder, sphere, pyramid, prism etc.Higher-dimensional shapes – there are few shapes express in dimensions greater than 3, yet we usually perform not study them in middle-level mathematics.

What are solids?

In geometry, there space various types of solids. Solids room three-dimensional shapes because they have three dimensions such as length, breadth and also height. The body which occupy room are dubbed solids.

Solid or 3D forms properties

Solids room classified in regards to their properties. To analysis characteristics and also properties that 3-D geometric shapes, count the variety of faces, edges, and vertices in assorted geometric solids. Allow us comment on the properties and also formulas for the different solid shapes.


Solid ShapeFigurePropertyVolume Formula

(Cubic Units)

Surface Area Formula

(Square Units)

Cube
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Face – square (6)

vertices – 8

Edges – 12

a36a2
Cuboid
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Face – Rectangle (6)

vertices – 8

Edges – 12

l × b × h2(lb+lh+hb)
Sphere
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Curved surface = 1

Edges = 0

Vertices = 0

(4/3)πr34πr2
Cylinder
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Flat surface ar = 2

Curved surface = 1

Face = 3

Edges =2

Vertices =0

πr2h2πr(r+h)
Cone
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Flat surface = 1

Curved surface ar = 1

Face = 2

Edges = 1

Vertices =1

(⅓)πr2hπr(r+l)

Solids Examples

Question 1:

Find the volume and also surface area the a cube whose side is 5 cm.

Solution:

Side, a = 5 cm

The volume the a cube formula is:

The volume that a cube = a3 cubic units

V = 53

V = 5 × 5 × 5

V =125 cm3

Therefore, the volume the a cube is 125 cubic centimetre

The surface area that a cube = 6a2 square units

SA = 6(5)2 cm2

SA = 6(25)

SA = 150 cm2

Therefore, the surface area the a cube is 150 square centimetre

Question 2:

Find the volume the the ball of radius 7 cm.

Solution:

Given radius of the round = r = 7 cm

Volume of round = 4/3 πr3

= (4/3) × (22/7) × 7 × 7 × 7

= 4 × 22 × 7 × 7

= 4312 cm3

Question 3:

Find the total surface area that a cuboid of size 8 centimeter × 5 centimeter × 7 cm.

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Solution:

Given dimensions of a cuboid: 8 centimeter × 5 cm × 7 cm

That means, size = together = 8 cm

Breadth = b = 5 cm

Height = h = 7 cm

Total surface area that a cuboid = 2(lb + bh + hl)

= 2<8(5) + 5(7) + 7(8)>

= 2(40 + 35 + 56)

= 2 × 131

= 262 cm2

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