Questions

It is useful to have a property of a material that is independent of the size of the sample and can be use to compare its elastic properties with another - this is called the Modulus of Elasticity for the material.

The modulus of elasticity is defined as:

Modulus of elasticity = Stress / Strain

There are three types of moduli. They are :

(a) the Young Modulus - tensile and compression longitudinal stress

(b) the shear modulus - a shearing stress

(c) the bulk modulus - volume changes of the specimen.

Amjad Ali Khan

From the given equations,

(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
(6)2=14 + 2(ab + bc + ca)
36 - 14 = 2(ab + bc + ca)
22/2 = ab + bc + ca
ab + bc + ca = 11

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
= (6) (14 - 11)
=(6)(3)
=18

Since, a3 + b3 + c3 - 3abc = 18

36 - 3abc = 18

-3abc = 18 - 36

-3abc = -18

abc = 6.

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