# Puzzles Questions

A) Balloon | B) Temperature |

C) Lift | D) Rain |

A) 3 | B) 6 |

C) 9 | D) 12 |

Explanation:

**From the given equations,**

$(\mathrm{a}+\mathrm{b}+\mathrm{c}{)}^{2}={\mathrm{a}}^{2}+{\mathrm{b}}^{2}+{\mathrm{c}}^{2}+2(\mathrm{ab}+\mathrm{bc}+\mathrm{ca})$

${\left(6\right)}^{2}=14+2(\mathrm{ab}+\mathrm{bc}+\mathrm{ca})$

36 - 14 = 2(ab + bc + ca)

22/2 = ab + bc + ca

ab + bc + ca = 11

${\mathrm{a}}^{3}+{\mathrm{b}}^{3}+{\mathrm{c}}^{3}-3\mathrm{abc}=(\mathrm{a}+\mathrm{b}+\mathrm{c})({\mathrm{a}}^{2}+{\mathrm{b}}^{2}+{\mathrm{c}}^{2}-\mathrm{ab}-\mathrm{bc}-\mathrm{ca})$

= (6) (14 - 11)

=(6)(3)

=18

Since, ${\mathrm{a}}^{3}+{\mathrm{b}}^{3}+{\mathrm{c}}^{3}-3\mathrm{abc}=18$

36 - 3abc = 18

-3abc = 18 - 36

-3abc = -18

**abc = 6.**