Question 52

The length of the longest diagonal that can be placed in a closed cube is $$50\sqrt{3}$$ cm. What is the total surface area of this cube?

Solution

The length of the longest diagonal that can be placed in a closed cube is $$50\sqrt{3}$$ cm.

diagonal of cube = $$\sqrt{\ 3}\times\ length\ of\ each\ side$$

$$50\sqrt{3} = \sqrt{\ 3}\times\ length\ of\ each\ side$$

$$50=\ length\ of\ each\ side$$

Total surface area of this cube = $$6\times\ \left(length\ of\ each\ side\right)^2$$

= $$6\times\ \left(50\right)^2$$

= $$6\times\ 2500$$

= 15000 $$cm^{2}$$

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