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

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Geometric Shapes

The geometrical figures classified based on 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 figure that has length and breadth as two dimensions. For instance – square, triangle, rectangle, parallelogram, trapezoid, rhombus, quadrilateral, polygon, circle etc.Three-dimensional shapes – things with length, breadth and height as three dimensions. For example – cube, cuboid, cone, cylinder, sphere, pyramid, prism etc.Higher-dimensional shapes – there are few shapes to express in dimensions higher than 3, but we usually carry out not study them in middle-level mathematics.

What room solids?

In geometry, there are various types of solids. Solids room three-dimensional shapes since they have actually three size such together length, breadth and also height. The body which occupy room are referred to as solids.

Solid or 3D shapes properties

Solids room classified in regards to their properties. To analysis characteristics and also properties of 3-D geometric shapes, count the variety of faces, edges, and also vertices in assorted geometric solids. Let us talk about the properties and also formulas because that 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 ar = 1

Curved surface ar = 1

Face = 2

Edges = 1

Vertices =1

(⅓)πr2hπr(r+l)

Solids Examples

Question 1:

Find the volume and surface area of a cube whose next is 5 cm.

Solution:

Side, a = 5 cm

The volume that a cube formula is:

The volume of a cube = a3 cubic units

V = 53

V = 5 × 5 × 5

V =125 cm3

Therefore, the volume of a cube is 125 cubic centimetre

The surface area the a cube = 6a2 square units

SA = 6(5)2 cm2

SA = 6(25)

SA = 150 cm2

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

Question 2:

Find the volume of 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 complete surface area the a cuboid of size 8 cm × 5 cm × 7 cm.

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Solution:

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

That means, length = together = 8 cm

Breadth = b = 5 cm

Height = h = 7 cm

Total surface area the 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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