Geometric Shapes in Solid Geometry
Geometric Shapes 
Formulas 
Capsule

Capsule Calculator
 Volume = πr^{2}((4/3)r + a)
 Surface Area = 2πr(2r + a)
 Circumference = 2πr
Also called a stadium of revolution. 
Circular Cone

Circular Cone Calculator
 Volume = (1/3)πr^{2}h
 Slant Height = √(r^{2} + h^{2})
 Lateral Surface Area = πrs = πr√(r^{2} + h^{2})
 Base Surface Area = πr^{2}
 Total Surface Area
= L + B = πrs + πr^{2} = πr(s + r) = πr(r + √(r^{2} + h^{2}))

Circular Cylinder

Circular Cylinder Calculator
 Volume = πr^{2}h
 Lateral Surface Area = 2πrh
 Top Surface Area = πr^{2}
 Bottom Surface Area = πr^{2}
 Total Surface Area
= L + T + B = 2πrh + 2(πr^{2}) = 2πr(h+r)

Conical Frustum

Conical Frustum Calculator
 Volume = (1/3)πh (r_{1}^{2} + r_{2}^{2} + (r_{1} * r_{2}))
 Slant Height = √((r_{1}  r_{2})^{2} + h^{2})
 Lateral Surface Area
= π(r_{1} + r_{2})s = π(r_{1} + r_{2})√((r_{1}  r_{2})^{2} + h^{2})
 Top Surface Area = πr_{1}^{2}
 Base Surface Area = πr_{2}^{2}
 Total Surface Area
= π(r_{1}^{2} + r_{2}^{2} + (r_{1} * r_{2}) * s)
= π[ r_{1}^{2} + r_{2}^{2} + (r_{1} * r_{2}) * √((r_{1}  r_{2})^{2} + h^{2}) ]

Cube

Cube Calculator
 Volume = a^{3}
 Surface Area = 6a^{2}
 Face Diagonal
(f) = a√2
 Diagonal (d) = a√3

Hemisphere

Hemisphere Calculator
 Volume = (2/3)πr^{3}
 Circumference = 2πr
 Curved Surface Area = 2πr^{2}
 Base Surface Area = πr^{2}
 Total Surface Area= (2πr^{2}) + (πr^{2}) = 3πr^{2}

Pyramid : Square

Pyramid Calculator
 Volume = (1/3)a^{2}h
 Slant Height (s) = √(h^{2} + (1/4)a^{2})
 Lateral Surface Area = a√(a^{2} + 4h^{2})
 Base Surface Area = a^{2}
 Total Surface Area
= L + B = a^{2} + a√(a^{2} + 4h^{2}))
= a(a + √(a^{2} + 4h^{2}))

Rectangular Prism

Rectangular Prism Calculator
 Volume = lwh
 Surface Area = 2(lw + lh + wh)
 Diagonal (d) = √(l^{2} + w^{2} + h^{2})

Sphere

Sphere Calculator
 Volume = (4/3)πr^{3}
 Circumference = 2πr
 Surface Area = 4πr^{2}

Spherical Cap

Spherical Cap Formulas
 Volume
= (1/6)πh(3a^{2} + h^{2})
= (1/3)πh^{2}(3R  h)
 Radius Base Circle = √h(2R  h)
 Circumference Base Circle = 2π√h(2R  h)
 Surface Area = 2πRh = π(a^{2} + h^{2})

Spherical Segment

Spherical Segment Formulas
 Volume = (1/6)πh(3a^{2} + 3b^{2} + h^{2})
 Top Surface Area = πb^{2}
 Bottom Surface Area = πa^{2}
 Lateral Surface Area = 2πRh
 Where R = sphere radius and
 R = √{ [ [(ab)^{2} + h^{2}] [(a+b)^{2} + h^{2}] ] / 4h^{2} }

Tube

Tube Calculator (Hollow Cylinder)
 Circumference, C:
 C_{1} = 2πr_{1}
 C_{2} = 2πr_{2}
 Lateral Surface Area, L, for a cylinder:
 L_{1} = 2πr_{1}h, the external surface area
 L_{2} = 2πr_{2}h, the internal surface area
 Area, A, for the end cross section of the tube:
 A_{1} = πr^{12} for the area enclosed by C_{1}
 A_{2} = πr^{22} for the area enclosed by C_{2}
 A = A_{1}  A_{2} = π(r^{12}  r^{22}) for the area of the solid cross section of the tube, the end, an annulus.
 Volume, V, (using volume for a cylinder):
 V_{1} = πr^{12}h for the volume enclosed by C_{1}
 V_{2} = πr^{22}h for the volume enclosed by C_{2}
 V = V_{1}  V_{2} = π(r^{12}  r^{22})h for the volume of the solid, the tube.
 Thickness of the tube wall, t:
