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Mensuration
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Mensuration
You'll learn here the basic concepts of Mensuration.

Space Figure
A space figure, also called three-dimensional figure is a figure which has depth in addition to width and height. Everyday Objects in every day life like a tennis ball, a box, and a redwood tree are all examples of space figures. Some common simple space figures include cubes, spheres, cylinders, prisms, cones, and pyramids etc. A space figure having all flat faces is called a polyhedron. A cube and a pyramid are both polyhedrons; but a sphere, cylinder, and cone are not.

Solids
Solids are three-dimensional objects, bound by one or more surfaces. When plane surfaces bind a solid, they are called its faces. The lines of intersection of adjacent faces are called edges of the solid.
For any regular solid with plane surfaces:
Remember: Number of faces + Number of vertices = Number of edges + 2
This formula is called Euler's formula.

Volume
Volume of solid figure is the amount of space enclosed by its bounding surfaces. Volume is measured in cubic units. 
Weight of a solid = Volume x Density
1 cubic meter = 10 x 10 x 10 cubic cm = 1000 cubic cm.

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Cube
A cube is a special case of a parallelepiped in which length, breadth and height are equal i.e. it is bound by six square faces.
Thus it has 6 equal-area faces and 12 equal-length edges.
If the length of one edge is l, the volume (V) of the cube is given by:
V = l3
Its surface area (A) is calculated by finding the area of one square:
l x l = l 2;
and multiplying it by 6:
6 x l 2
A = 6l2

Example: Three cubes whose edges measure 4 cm, 5 cm and 6 cm respectively to form a single cube. Find its edge. Also, find the surface area of the new cube.
Solution Let x cm be the edge of the new cube. Then,
Volume of the new cube = Sum of the volumes of three cubes
x3 = 43 + 53 + 63 = 64 + 125 + 216
x3 = (405)3
x = 315
Edge of the new cube is 315 cm long.
Surface area of the new cube = 6 x2 = 6 * (315)2 cm2 = 810 cm2.
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