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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