In Geometry, the form or the figure that has three (even higher) dimensions, are known as solids or three-dimensional shapes. The study of the properties, volume and surface area of three-dimensional shapes is referred to as Solid Geometry. Let united state go ahead and focus an ext on the research of geometrical solids.

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Geometric Shapes

The geometrical figures classified based on the dimensions are as follows:

Zero dimensional shape – A point.One dimensional shape – A heat that has actually a length as its dimension.Two-dimensional shapes – A number that has actually length and also breadth as 2 dimensions. For instance – square, triangle, rectangle, parallelogram, trapezoid, rhombus, quadrilateral, polygon, circle etc.Three-dimensional forms – things with length, breadth and also height as 3 dimensions. For example – cube, cuboid, cone, cylinder, sphere, pyramid, prism etc.Higher-dimensional shapes – there are few shapes expressed in dimensions higher than 3, however we usually execute not examine them in middle-level mathematics.

What room solids?

In geometry, there are various types of solids. Solids room three-dimensional shapes due to the fact that they have actually three size such as length, breadth and also height. The bodies which occupy an are are called solids.

Solid or 3D shapes properties

Solids are classified in regards to their properties. To analyze characteristics and properties that 3-D geometric shapes, count the number of faces, edges, and also vertices in various geometric solids. Let us talk about the properties and formulas for the various 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 = 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 side is 5 cm.

Solution:

Side, a = 5 cm

The volume of a cube formula is:

The volume that a cube = a3 cubic units

V = 53

V = 5 × 5 × 5

V =125 cm3

Therefore, the volume that 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 ar area the 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 ball = 4/3 πr3

= (4/3) × (22/7) × 7 × 7 × 7

= 4 × 22 × 7 × 7

= 4312 cm3

Question 3:

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

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Solution:

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

That means, size = together = 8 cm

Breadth = b = 5 cm

Height = h = 7 cm

Total surface ar 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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