Geometric Shapes

capsule

Capsule Calculator

  • Volume = Ï€r2((4/3)r + a)
  • Surface Area = 2Ï€r(2r + a)
  • Circumference = 2Ï€r

Also called a stadium of revolution.

cone

Circular Cone Calculator

  • Volume = (1/3)Ï€r2h
  • Slant Height = √(r2 + h2)
  • Lateral Surface Area = Ï€rs = Ï€r√(r2 + h2)
  • Base Surface Area = Ï€r2
  • Total Surface Area
    = L + B = Ï€rs + Ï€r2 = Ï€r(s + r) = Ï€r(r + √(r2 + h2))
frustum

Conical Frustum Calculator

  • Volume = (1/3)Ï€h (r12 + r22 + (r1 * r2))
  • Slant Height = √((r1 – r2)2 + h2)
  • Lateral Surface Area
    = Ï€(r1 + r2)s = Ï€(r1 + r2)√((r1 – r2)2 + h2)
  • Top Surface Area = Ï€r12
  • Base Surface Area = Ï€r22
  • Total Surface Area
    = Ï€(r12 + r22 + (r1 + r2) * s)
    = Ï€[ r12 + r22 + (r1 + r2) * √((r1 – r2)2 + h2) ]
cubic solid

Cube Calculator

  • Volume = a3
  • Surface Area = 6a2
  • Face Diagonal (f) = a√2
  • Diagonal (d) = a√3
hemisphere

Hemisphere Calculator

  • Volume = (2/3)Ï€r3
  • Circumference = 2Ï€r
  • Curved Surface Area = 2Ï€r2
  • Base Surface Area = Ï€r2
  • Total Surface Area= (2Ï€r2) + (Ï€r2) = 3Ï€r2
pyramid

Pyramid Calculator

  • 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))
rectangle-solid

Rectangular Prism Calculator

  • Volume = lwh
  • Surface Area = 2(lw + lh + wh)
  • Diagonal (d) = √(l2 + w2 + h2)
sphere

Sphere Calculator

  • Volume = (4/3)Ï€r3
  • Circumference = 2Ï€r
  • Surface Area = 4Ï€r2
sphericalcap

Spherical Cap Formulas

  • Volume
    = (1/6)Ï€h(3a2 + h2)
    = (1/3)Ï€h2(3R – h)
  • Radius Base Circle = √h(2R – h)
  • Circumference Base Circle = 2π√h(2R – h)
  • Surface Area = 2Ï€Rh = Ï€(a2 + h2)
sphericalsegment

Spherical Segment Formulas

  • Volume = (1/6)Ï€h(3a2 + 3b2 + h2)
  • Top Surface Area = Ï€b2
  • Bottom Surface Area = Ï€a2
  • Lateral Surface Area = 2Ï€Rh
  • Where R = sphere radius and
  • R = √{ [ [(a-b)2 + h2] [(a+b)2 + h2] ] / 4h2 }
triangular prism

Triangular Prism Formulas

  • Volume = (1/4)h √[(a+b+c)(b+c-a)(c+a-b)(a+b-c)]
  • Top Surface Area = (1/4) √[(a+b+c)(b+c-a)(c+a-b)(a+b-c)]
  • Bottom Surface Area = (1/4) √[(a+b+c)(b+c-a)(c+a-b)(a+b-c)]
  • Lateral Surface Area = h(a+b+c)
  • Total Surface Area = Top Surface Area + Bottom Surface Area + Lateral Surface Area
tube

Tube Calculator (Hollow Cylinder)

  • Circumference, C:
  • Lateral Surface Area, L, for a cylinder:
    • L1 = 2Ï€r1h, the external surface area
    • L2 = 2Ï€r2h, the internal surface area
  • Area, A, for the end cross section of the tube:
    • A1 = Ï€r12 for the area enclosed by C1
    • A2 = Ï€r22 for the area enclosed by C2
    • A = A1 – A2 = Ï€(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 = Ï€r12h for the volume enclosed by C1
    • V2 = Ï€r22h for the volume enclosed by C2
    • V = V1 – V2 = Ï€(r12 – r22)h for the volume of the solid, the tube.
  • Thickness of the tube wall, t:

Cite this content, page or calculator as:

Zaheer Ahmed “Geometric Shapes and Formulas in Solid Geometry” at https://calculatorcave.com/calculators/geometry-solids/geometricshapes/ from CalculatorCave, https://calculatorcave.com – Online Calculators