Question 75
Find the length of the diagonal of a closed cube whose total surface area is 96 $$m^{2}$$.
Solution
total surface area of a closed cube is 96 $$m^{2}$$.
total surface area of a closed cube = $$6\times\ \left(side\right)^2$$
$$96 = 6\times\ \left(side\right)^2$$
$$16=\ \left(side\right)^2$$
$$4^2=\ \left(side\right)^2$$length of the side of closed cube = 4 m
length of the diagonal of a closed cube = $$\sqrt{\ 3}\times\ side$$
= $$\sqrt{\ 3}\times\ 4$$
= $$4\sqrt{\ 3}$$ m
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