Solid Geometry

Formulas

• Volume = πr2((4/3)r + a)

• Surface Area = 2πr(2r + a)

• Circumference = 2πr

• Volume = (1/3)πr2h

• Slant Height = √(r2 + h2)

• Lateral Surface Area = πrs = πr√(r2 + h2)

  • Base Surface Area = πr2

• Total Surface Area

• = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

• Volume = πr2h

• Lateral Surface Area = 2πrh

  • Top Surface Area = πr2

• Bottom Surface Area = πr2

• Total Surface Area

• = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

• Volume = (1/3)πh (r12 + r22 + (r1 * r2))

• Slant Height = √((r1 - r2)2 + h2)

• Lateral Surface Area

• = π(r1 + r2)s = π(r1 + r2)√((r1 - r2)2 + h2)

  • Top Surface Area = πr12

  • Base Surface Area = πr22

• Total Surface Area

• = π(r12 + r22 + (r1 * r2) * s)

• = π[ r12 + r22 + (r1 * r2) * √((r1 - r2)2 + h2) ]

  • Volume = a3

  • Surface Area = 6a2

• Face Diagonal (f) = a√2

• Diagonal (d) = a√3

  • Volume = (2/3)πr3

  • Circumference = 2πr

  • Curved Surface Area = 2πr2

  • Base Surface Area = πr2

  • Total Surface Area= (2πr2) + (πr2) = 3πr2

  • Volume = (1/3)a2h

  • Slant Height (s) = √(h2 + (1/4)a2)

  • Lateral Surface Area = a√(a2 + 4h2)

  • Base Surface Area = a2

  • Total Surface Area

  • = L + B = a2 + a√(a2 + 4h2))

  • = a(a + √(a2 + 4h2))

  • Volume = lwh

  • Surface Area = 2(lw + lh + wh)

  • Diagonal (d) = √(l2 + w2 + h2)

  • Volume = (4/3)πr3

  • Circumference = 2πr

  • Surface Area = 4πr2

  • Volume

  • = (1/6)πh(3a2 + h2)

  • = (1/3)πh2(3R - h)

  • Radius Base Circle = √h(2R - h)

  • Circumference Base Circle = 2π√h(2R - h)

  • Surface Area = 2πRh = π(a2 + h2)

  • Volume = (1/6)πh(3a2 + 3b2 + h2)

  • Top Surface Area = πb2

  • Bottom Surface Area = πa2

  • Lateral Surface Area = 2πRh

  • Where R = sphere radius and

  • R = √{ [ [(a-b)2 + h2] [(a+b)2 + h2] ] / 4h2 }

  • Circumference, C:

    • • C1 = 2πr1

      • C2 = 2πr2

  • Lateral Surface Area, L, for a cylinder:

    • • L1 = 2πr1h, the external surface area

      • L2 = 2πr2h, the internal surface area

  • Area, A, for the end cross section of the tube:

    • • A1 = πr12 for the area enclosed by C1

      • A2 = πr22 for the area enclosed by C2

• • • A = A1 - A2 = π(r12 - r22) for the area of the solid cross section of the tube, the end, an annulus.

• • Volume, V, (using volume for a cylinder):

    • • V1 = πr12h for the volume enclosed by C1

      • V2 = πr22h for the volume enclosed by C2

• • • V = V1 - V2 = π(r12 - r22)h for the volume of the solid, the tube.

• • Thickness of the tube wall, t:

    • • t = r1 - r2