Chapter 10: Measurement,Area&Volume

Allie G

Formulas

Area of a parallelogram: A = b*h

Area of a trapezoid: A = 1/2 (b1 + b2)h

Area of a circle: A = pi r²

Surface Area of a Prism: S=2B + Ph

Surface Area of a Cylinder: S = 2B+ Ch = 2*pi*r²+ 2*pi*rh

Surface Area of a Pyramid: S = B + 1/2*p*l

Surface Area of a Cone: S= pi*r² + pi*r*l

Section 1: Areas of a Parallelograms and Trapezoids

Section 2: Area of a Circle

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Words: The area of a circle is the product of pi and the square of the radius.


Algebra: A = pi*r²


Numbers: A = pi*6²= 36*pi cm²

Area of a circle

Section 3: Three-Dimensional Figures

A solid is a three dimensional figure that encloses a part of space. A polyhedron is a solid that is enclosed by polygons. A polyhedron has only flat surfaces. The polygons that from a polyhedron are called faces.


Pentagonal Pyramid:


Faces: 6


Vertex: 6


Edges: 10


Euler's Formula:

Faces + Edges = Vertices + 2

Section 4: Surface Areas of Prisms and Cylinders

Net: A two dimensional pattern that forms a solid when folded


Surface Area: The sum of the areas of its faces.


Lateral Surface Area of a Cylinder: Its equal to the area of its curved surface, This surface becomes a rectangle in the net of the cylinder, with length equal to the circumference of the base

Cylinder Volume and Surface Area

Section 5: Surface Areas of Pyramids and Cones

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  1. Slant Height (l): of a regular pyramid is the height of a lateral face, that is, any face that is not the base
  2. S = B + 1/2*pl
  3. Surface Area = S
  4. Area of the Base = B
  5. Perimeter = P
  6. Slant Height = L

Surface Area of a Pyramid: find the perimeter of the base

P = 8 + 8 + 8 = 24

Substitute into the formula for the surface area

S = B + 1/2Pl

= 27.2 + 1/2*24*6

= 99.7 m²

Geometry Sec 12-3 Surface Areas of Pyramids and Cones

Section 6: Volumes of Prisms and Cylinders

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Words: The volume of a prism is the product if the area of the base B and the height h


Algebra: V = Bh


Volume of a Prism

V =Bh

= lwh

= 12*8*2

= 192 in^3


Volume of a Cylinder:

V =Bh

= pi*r²h

= pi*3^2*9

= 81*pi

= 254.469 cm^3

12.4 Volumes of Prisms and Cylinders (Lesson)

Section 7: Volumes of Pyramids and Cones

The Volume of a pyramid and a cone is one third the product of the area of the base B and the height h


Algebra: 1/3Bh


Volume of a Pyramid:

V = 1/3Bh

= 1/3 *30²*15

= 4500 ft^3


Volume of a Cone:

V = 1/3*pi*r^2h

= 1/3*pi*6²*12

= 144*pi

= 452.389 ft ^3

Volume of Cones and Pyramids 128-4.14
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