Volume Formulas

The standard notation for volume is V. With it we measure the quantity(for example water), that can be filled in a figure. Only figures in the space have volume. For example triangles, squares do not have volume, but a ball have volume(because it can be filled with water).

Cube

Cube is a parallelepiped that all sides are squares(all sides are the same).

cube

If a side of a cube is a then the volume formula is:

$V = a \cdot a \cdot a = a^3$

Rectangular parallelepiped

rectangular parallelepiped

Rectangular parallelepiped is a figure that all sides are rectangles.
If the sides of the rectangle at the bottom are a and b and the height of the parallelepiped is c (the third edge of the rectangular parallelepiped).
The volume formula is:

$V = a \cdot b \cdot c$

Parallelepiped

parallelepiped

Parallelepiped is a figure that all sides are parallelograms. If the area of the bottom is A and the height of the parallelepiped is h.
The volume formula is:

$V = A \cdot h$

Pyramid

pyramid

Pyramid is a figure with a bottom triangle, parallelogram(square, rectangle), or other n-angle figure and sides are triangles.
If the area of the bottom is A and the height of the pyramid is long h.
The volume formula is:

$V = \frac{1}{3} \cdot A \cdot h$

Cone

cone

Cone is a figure with a bottom circle and have one top like a pyramid.
If the area of the bottom is A and the height of the cone is h.
The volume formula is:

$V = \frac{1}{3} \cdot A \cdot h = \frac{1}{3} \cdot \pi \cdot r^2\cdot h$

Sphere

sphere

Sphere is a globe, or a ball.
It has a central point of called "center" of the sphere. If the length of the radius(the length from the central point to any point on the surface of the sphere) is R. The volume formula is:

$V = \frac{4}{3}\cdot \pi \cdot R \cdot R \cdot R = \frac{4}{3} \cdot \pi \cdot R^3$

Cylinder

cylinder

Cylinder is figure that has two identical and parallel circular bases.
If the radius of the bottom is r and the height(the distance between the bottoms) of the cylinder is h.
The volume formula is:

$V = \pi \cdot r \cdot r \cdot h = \pi \cdot r^2 \cdot h$

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