Volume and Surface of some Common Solids
Surface and volume of solids like rectangular prism, cylinder, pyramid, cone and sphere
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Rectangular Prism
Volume of a rectangular prism can be expressed as
V = l b h (1)
where
V = volume of solid (m3, ft3)
l = length of rectangular prism (m, ft)
b = width of rectangular prism (m, ft)
h = height of rectangular prism (m, ft)
Surface of a rectangular prism can be expressed as
A = 2 (b h + h l + l b) (1b)
where
A = surface area of solid (m2, ft2)
Cylinder
Volume of a cylinder can be expressed as
V = π r2 h (2)
where
r = radius of cylinder (m, ft)
h = height of cylinder (m, ft)
Surface of a cylinder can be expressed as
A = 2 π r h + 2 π r2 (2b)
Pyramid
Volume of a pyramid can be expressed as
V = 1/3 l Ab (3)
where
Ab = area of base (m2, ft2)
h = perpendicular height of pyramid (m, ft)
Surface of a cylinder can be expressed as
A = ∑ sum of areas of triangles forming sides + Ab (3b)
where
the surface areas of the triangular faces will have different formulas for different shaped bases
Cone
Volume of a cone can be expressed as
V = 1/3 π r2 h (4)
where
r = radius of cone base (m, ft)
h = height of cone (m, ft)
Surface of a cone can be expressed as
A = π r l + π r2 (4b)
where
l = (r2 + h2)1/2 = length of cone side (m, ft)
Sphere
Volume of a sphere can be expressed as
V = 4/3 π r3 (5)
where
r = radius of sphere (m, ft)
Surface area of a sphere can be expressed as
A = 4 π r2 (5b)
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