Unit 10: Measurement, Area, Volume

by Nathaniel D'Amour

Areas of Parallelograms and Trapezoids

Parallelograms: A = bh


Trapezoids: A = 1/2(b1 + b2)h


Examples:


  • Parallelograms:
  • 57,800 = 680 * 85
  • 571,500 = 635 * 900
  • 57,956,250 = 7,025 * 8,250
  • Trapezoids:
  • 7,250 = 1/2 * (65 + 80) * 100
  • 1,812.2 = 1/2 * (85 + 60) * 25
  • 685,000 = 1/2 * (605 + 765) * 1,000

Areas of Circles

A = 3.14 * r^2


Examples:

  • 31,400 = 3.14 * 100^2
  • 9498.5 = 3.14 * 55^2
  • 196,250 = 3.14 * 250^2

3-Dimensional Figures

  • Prism (includes bases, vertices, and edges)
  • Pyramid (includes bases, vertices, and edges)
  • Cylinder (includes 1 base)
  • Cone (includes 1 base)
  • Sphere (includes 1 center)

Surface Area of Prisms & Cylinders

Prisms: S = 2B + Ph


Cylinders: S = (2* 3.14 * r^2) + (2 * 3.14 * r * h)


Examples:

  • Prisms:
  • 590 = (2 * 95) + (8 * 50)
  • 700 = (2 * 65) + (95 * 6)
  • 3,100 = (2 * (1/2 * 25 * 60)) + ((15 + 15+ 50) * 20)
  • Cylinders:
  • 1,909.12 = (2 * 3.14 * 8^2) + (2 * 3.14 * 6 * 30)
  • 39,564 = (2 * 3.14 * 60^2) + (2 * 3.14 * 60 * 45)
  • 770,085 = (2 * 3.14 * 75^2) + (2 * 3.14 * 75 * 1,560)

Surface Area of Pyramids & Cones

Pyramids: S = B + 1/2Pl


Cones: S = (3.14 * r^2) + (3.14 * r * l)


Examples:

  • Pyramids:
  • 3,500 = 1,500 + (1/2 * 40 * 100)
  • 9,960 = 8,560 + (1/2 * 35 * 80)
  • 15,665 = 5,815 + (1/2 * 20 * 985)
  • Cones:
  • 13,188 = (3.14 * 60^2) + (3.14 * 60 * 10)
  • 137,375 = (3.14 * 70^2) + (3.14 * 70 * 555)
  • 302,617.5 = (3.14 * 15^2) + (3.14 * 15 * 6,410)

Volumes of Prisms & Cylinders

Prisms: V = B = (l * w | 1/2 * l * w) * h


Cylinders: V = (B = 3.14 * r^2) * h


Examples:


  • Prisms:
  • 8,500 = (1/2 * 85 * 20) * 10
  • 1,312,500 = (25 * 875) * 60
  • 2,142,000 = (595 * 120) * 30
  • Cylinders:
  • 1,758.4 = (3.14 * 4^2) * 35
  • 8,462.3 = (3.14 * 7^2) * 55
  • 9,043.2 = (3.14 * 6^2) * 80

Volumes of Pyramids & Cones

Pyramids: V = 1/3 * (B^2 * h)


Cones: V = 1/3 * ((B = 3.14 * r^2) * h)


Examples:

  • Pyramids:
  • 2,083.4 = 1/3 * (25^2 * 10)
  • 37,333.4 = 1/3 * (40^2 * 70)
  • 74,666.7 = 1/3 * (80^2 * 35)
  • Cones:
  • 282.6 = 1/3 * ((3.14 * 3^2) * 30)
  • 1,695.6 = 1/3 * ((3.14 * 6^2) * 45)
  • 3,949.1 = 1/3 ((3.14 * 7^2) * 77)