home
Mission
//////
home
//////

3.1 Geometry

Tags
Circle
Geometry
Area
Arc
Length
Circumference
Sector

Midpoint and distance:

To find the midpoint of two points (x1,y1,z1)(x_1,y_1,z_1) and (x2,y2,z2)(x_2,y_2,z_2) in three-dimensional space:
(x1+x22,y1+y22,z1+z22)(\frac{x_1+x_2}2,\frac {y_1+y_2}2,\frac {z_1+z_2}2)
The distance d between two points (x1,y1,z1)(x_1,y_1,z_ 1) and (x2,y2,z2)(x_2,y_2,z_2) in three-dimensional space:
d=(x2−x1)2+(y2−y1)2+(z2−z1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}

Circle geometry:

1.
Circumference C=2πrC=2\pi r
2.
Area A=πr2A=\pi r^2
3.
Length of arc l=rθl = r\theta
4.
Area of sector A=12θr2=12rlA =\frac 12\theta r^2 =\frac 12rl
5.
In a polar coordinate system we have: x=rcos⁡θx = r \cos\theta and y=rsin⁡θy =r\sin\theta.
Figure 3.1.1 Components of a circle
Figure 3.1.2 Unit circle

3-dimensional shapes:

Volume: The amount of space enclosed within a 3D object
1.
Pyramid: V=13AbasehV=\frac 13A_{base}h
2.
Cone: V=13πr2hV=\frac 13\pi r^2h
3.
Cylinder: V=πr2hV=\pi r^2h
4.
Sphere: v=43πr3v=\frac 43\pi r^3
5.
Rectangular prisms: V=lwhV=lwh
Surface Area: The total area of all the surfaces of a 3D object.
1.
Cylinder: S=2πrh+2πr2S=2\pi rh+2\pi r^2
2.
Sphere: S=4πr2S=4\pi r^2
3.
Cone: S=πrs+πr2S=\pi rs+\pi r^2
3.1 Geometry
done
https://docs.google.com/forms/d/e/1FAIpQLSeE2Gx2o1VbHby-v-R7jpuZvDw20GuZJok4ozrj4_aZyIgPuA/viewform
3.1 Geometry