The volume of a solid is the amount of space it occupies. It is associated with the number of cubes contained in it.
Capacity is the amount that can be contained.
Cube
The cube is a special kind of rectangular solid where the length, the width and height are equal.
In other words the faces are in the form of square. So its volume is
V = s^3
where s = edge of the cube
s^3 = s • s • s
Rectangular Solids
The base is rectangular
V = Bh
B = lw
V = lwh
The base is a square
V = Bh
B = s^2
V = s^2h
Prism
A prism is a solid with two congruent parallel bases and whose lateral faces are parallelogram.
The faces included between the two bases are called lateral faces.
Prisms are named from the figures of their bases; as triangular prism, rectangular prism, etc. , according as their bases are triangles, rectangles, etc.
The volume of a prism is the product of the area of the base and height, that is
V = Bh
For a triangular prism, the bases are congruent triangles. Thus, the area of the base is
B = 1/2 ba or B = ba/2
Then its volume is
V = ( ba ÷ 2) h
where
b = side of the triangular base
a = altitude of the triangular base
h = height of the prism
For a rectangular prism, the bases are congruent rectangles. So
V = Bh or V = lwh
Cylinder
A cylinder is a solid bounded by a closed cylindrical surface and two parallel planes. Although there are different cylinders, we will limit our discussions to right circular cylinder, wherein the bases are circles and the sides are perpendicular to the bases.
The volume of a cylinder is the product of the area of the base and its height, or
V = Bh
B = πr^2 or B = ( πd^2) ÷ 4
Since base is a circle and 2r = d
V = πr^2h or V = ( πd^2 ÷ 4 ) h
Cone
V = 1/3 Bh
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