Menu Close

How-much-the-long-of-the-diagonal-space-if-total-area-of-a-cube-is-216-cm-2-




Question Number 157981 by zainaltanjung last updated on 30/Oct/21
How much the long of the diagonal   space , if  total area of a cube is   216 cm^2 .
$$\mathrm{How}\:\mathrm{much}\:\mathrm{the}\:\mathrm{long}\:\mathrm{of}\:\mathrm{the}\:\mathrm{diagonal} \\ $$$$\:\mathrm{space}\:,\:\mathrm{if}\:\:\mathrm{total}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{is} \\ $$$$\:\mathrm{216}\:\mathrm{cm}^{\mathrm{2}} . \\ $$
Answered by cherokeesay last updated on 30/Oct/21
the area of one face of cube :  216 ÷ 6 = 36 cm^2   (a = 6cm)is a side of square.  d is a diagonal  d^2  = a^2  + (a(√2))^2  ⇒  d=(√(a^2 +2a^2 ))=a(√3)=6×1,732=10,392 cm
$${the}\:{area}\:{of}\:{one}\:{face}\:{of}\:{cube}\:: \\ $$$$\mathrm{216}\:\boldsymbol{\div}\:\mathrm{6}\:=\:\mathrm{36}\:{cm}^{\mathrm{2}} \\ $$$$\left({a}\:=\:\mathrm{6}{cm}\right){is}\:{a}\:{side}\:{of}\:{square}. \\ $$$${d}\:{is}\:{a}\:{diagonal} \\ $$$${d}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:\left({a}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \:\Rightarrow \\ $$$${d}=\sqrt{{a}^{\mathrm{2}} +\mathrm{2}{a}^{\mathrm{2}} }={a}\sqrt{\mathrm{3}}=\mathrm{6}×\mathrm{1},\mathrm{732}=\mathrm{10},\mathrm{392}\:{cm} \\ $$$$ \\ $$
Commented by zainaltanjung last updated on 30/Oct/21
Ok.it′s true sir.good job
$$\mathrm{Ok}.\mathrm{it}'\mathrm{s}\:\mathrm{true}\:\mathrm{sir}.\mathrm{good}\:\mathrm{job} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *