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Solid Geometry

Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

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Page 1: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Solid Geometry

Page 2: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Three Dimensions

Solid Geometry is the geometry of three-dimensional spaceIt is called three-dimensional, or 3D because there are three dimensions: width, depth and height.

Page 3: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Polyhedron

A geometric object with flat faces and straight edges.

each face is a polygon.

Page 4: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Polyhedron

FACE: Polygon shaped sides of a polyhedron

EDGE: Line segment formed by intersection of two faces

VERTEX: Point where three or more edges meet

Page 5: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Base

The surface that a solid object stands on – or the bottom line of a shape such as

a triangle or rectangle.

Page 6: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Polyhedron

Just like a 2D polygon a Polyhedron can be regular

Page 7: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Polyhedron

…or Irregular

Page 8: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Polyhedron

A Polyhedron can also be semi-Regular

Page 9: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Polyhedron

Just like a 2D polygon, a polyhedron can be convex

Page 10: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Polyhedron

…or concave

Page 11: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Prism

A solid object that has two identical bases and all flat sides.The shape of the bases give the prism it’s name– "triangular

prism“It is a polyhedron.

Page 12: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Pyramid

A solid object where:

* The base is a polygon (a straight-sided shape)

* The sides are triangles which meet at the top (the apex).

It is a polyhedron.

Page 13: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cylinder

A cylinder is a solid object with:

* two identical flat circular (or elliptical) ends

* and one curved side.

Page 14: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cone

A solid (3-dimensional) object that has – a circular base– and one vertex

Page 15: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Sphere

A solid (3-dimensional) object that has one

curved side

Page 16: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Prisms & Pyramids

Type Examples Properties

Triangular Prism

● 5 faces 2 triangular bases 3 rectangular faces● 9 edges● 6 vertices

Rectangular Prism

6 faces 2 rectangular bases 4 rectangular faces● 12 edges● 8 vertices

Cube

● 6 faces 2 square bases 4 square faces● 12 edges● 8 vertices

Square Pyramid

● 5 faces 1 square base 4 triangular faces● 8 edges● 5 vertices

Triangular Pyramid

● 4 faces 1 triangular base 3 triangular faces● 6 edges● 4 vertices

Page 17: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Three Dimensional Figures with Curved Surfaces

Type Example Properties

Cylinder● 2 circular bases

● 1 curved surface

Cone● 1 circular base

● 1 curved surface● 1 vertex

Sphere ● 1 curved surface

Page 18: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

VOLUME

Page 19: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Prism

V=BhB: Area of the baseh: height/length of the prism

Page 20: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Prism

V=Bh V= (Area of Triangle) * hV= (½bh) * hV= (½*19*24) *47V=(228) * 47V= 10,716 cm3

Page 21: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Prism

V=Bh V= (Area of Rect.) * hV= (bh) * hV= (2 * 3) * 6V=(6) * 6V= 36 ft3

Page 22: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cylinder

V=BhB: Area of the baseh: height/length of the prism

Page 23: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cylinder

V=Bh V= (Area of Circle) * hV= (πr2) * hV= (π * 32) *10V=(π * 9) * 10V= (28.26) * 10V= 282.6 cm3

Page 24: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cylinder

V=Bh V= (Area of Circle) * hV= (πr2) * hV= (π * 52) *21V=(π * 25) * 21V= (78.5) * 21V= 1,648.5 ft3

Page 25: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Pyramid

V=1/3BhB: Area of the baseh: height/length of the prism

Page 26: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Pyramid

V=1/3Bh V= 1/3(Area of Tri.) * hV= 1/3 * (½bh) * hV= 1/3 * (½* 6 * 4) *5V= 1/3 * (12) * 5V= 1/3 * 60V= 20 cm3

Page 27: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Pyramid

V=1/3Bh V= 1/3(Area of Sq.) * hV= 1/3 * (b * h) * hV= 1/3 * (5 * 5) *10V= 1/3 * (25) * 10V= 1/3 * 250V= 250/3 units3

Page 28: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cone

V=1/3BhB: Area of the baseh: height/length of the prism

Page 29: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cone

V=1/3Bh V= 1/3(Area of Circle)* hV= 1/3(πr2) * hV= 1/3(π * 1.52) *5V=1/3(π * 2.25) * 5V= 1/3(7.065) * 5V= 11.78 in3

Page 30: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Cone

V=1/3Bh V= 1/3(Area of Circle)* hV= 1/3(πr2) * hV= 1/3(π * 82) * 22V= 1/3(π * 64) * 22V= 1/3(200.96) * 22V= 1,473.71 cm3

Page 31: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Sphere

V=4/3 πr3

Page 32: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Sphere

V=4/3 πr3 V= 4/3 πr3

V= 4/3 * π * 143

V= 4/3 * π * 2744V= 4/3 * 8,616.16V= 11,488.21 cm3

Page 33: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Sphere

V=4/3 πr3 V= 4/3 πr3

V= 4/3 * π * 33

V= 4/3 * π * 27V= 4/3 * 84.78V= 113.04 cm3

Page 34: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

SURFACE AREA

Page 35: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Surface Area

The sum of the area of the bases and lateral surfaces

Page 36: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Prism

SA=2B+PhB: Area of the baseP: Perimeter of a baseh: height/length of the prism

Page 37: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Prism

SA=2B+Ph SA=2(Area of Rect.)+PhSA= 2(bh) + PhSA=2(3*2)+ (3+2+3+2)5SA=2(6) + (10)5SA= 12 + 50SA= 62 cm2

Page 38: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Prism

SA=2B+Ph SA=2(Area of Tri.)+PhSA= 2(1/2bh) + PhSA=2(1/2*3*8) +

(3+8+√73)7SA=2(12) + (11+√73)5SA= 24 + 55 + 5√73SA= 79 + 5√73 m2

SA = 121.72 m2

Page 39: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Cylinder

SA=2B+ChB: Area of the baseC: Circumference of a baseh: height/length of the cylinder

Page 40: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Cylinder

SA=2B+Ch SA=2(Area of Circ.)+ChSA= 2(πr2) + (2πr)hSA=2(π*152)+(2*π*15)48SA= 2(225π) + (30π)48SA= 1413 + 4521.6SA= 5934.6 cm2

Page 41: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Cylinder

SA=2B+Ch SA=2(Area of Circ.)+ChSA= 2(πr2) + (2πr)hSA=2(π*32)+(2*π*3)*9SA= 2(9π) + (6π)*9SA= 56.52 + 169.56SA= 226.08 cm2

Page 42: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Pyramid

SA=B + ½PsB: Area of the baseP: Perimeter of a bases: slant height of the lateral side

Page 43: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Pyramid (& Cone)

What is “slant height”?

Page 44: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Pyramid

SA=B + ½Ps SA=(Area of Rect.)+½PsSA= (bh) + ½PsSA=(12*12) + ½(12+12+12+12)*√136SA= (144) + ½ (48)*√136SA= 144 + 24√136SA= 423.89 units2

Page 45: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Pyramid

SA=B + ½Ps SA=(Area of Rect.)+½PsSA= (bh) + ½PsSA=(16*10) + ½(16+10+16+10)* 17SA= (160) + ½ (52)*17SA= 160 + 442SA= 602 in210 in

Page 46: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Cone

SA=B + ½CsB: Area of the baseP: Circumference of a bases: slant height of the lateral side

Page 47: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Cone

SA=B + ½Cs SA=(Area of Circ.)+½CsSA= (πr2) + ½(2πr)sSA= (πr2) + (πr)sSA= (π62) + (π6)10SA= 36π + 60πSA= 96πSA= 301.59 in2

Page 48: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Right Cone

SA=B + ½Cs SA=(Area of Circ.)+½CsSA= (πr2) + ½(2πr)sSA= (πr2) + (πr)sSA= (π0.62) + (π0.6)2SA= .36π + 1.2πSA= 1.56πSA= 4.9 ft2

Page 49: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Sphere

SA=4πr2

r: radius

Page 50: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Sphere

SA=4πr2 SA= 4πr2

SA= 4*π*42

SA= 4*π*16SA= 64πSA= 200.96 units2

Page 51: Solid Geometry Three Dimensions Solid Geometry is the geometry of three- dimensional space geometry It is called three- dimensional, or 3D because there

Sphere

SA=4πr2 SA= 4πr2

SA= 4*π*322

SA= 4*π*1024SA= 4096πSA= 12,861.44 units2