Mensuration

 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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