Question

$$\text{The length of the diagonal of a cube is}$$ $$8\sqrt {3} cm$$$$\text{. Find its:}$$

$$\text{(i) Edge }$$

$$\text{(ii) Total surface area }$$

$$\text{(iii) Volume}$$

$$\text{(Diagonal of a cube = }$$ $$\text{edge}$$ $$\sqrt{3}$$)

Answer 1

$$\textbf{Step-1: Apply formula of diagonal of cube}$$

$$\text{Diagonal of a cube = }$$ $$\text{edge}\times \sqrt{3}$$

$$\text{Let length of edge be =}$$ $$a$$

$$\text{so}$$ $$\sqrt {3}a = 8\sqrt {3}$$

$$\text{a = 8 cm}$$

$$\textbf{Step-2:}$$ $$\textbf{ Apply formula of total surface area of cube.}$$

$$\text{TSA = 6a}^{2}$$

$$\Rightarrow \text{TSA = 6 $\times$ 8}^{2}$$

$$\Rightarrow \text{TSA = 6$\times$ 64}$$

$$\Rightarrow \text{TSA = 384 cm}^{2}$$

$$\textbf{Step-3:}$$ $$\textbf {Apply formula of volume of cube.}$$

$$\text{Volume of cube = a}^{3}$$.

$$\Rightarrow \text{Volume of cube = 8}^{3}$$.

$$\Rightarrow \text{Volume of cube = 512 cm}^{3}$$.

$$\textbf{Hence Edge, Total surface area and Volume of cube is 8}$$$$\boldsymbol{\ cm}, $$$$\textbf{ 384}$$$$\boldsymbol{\ cm^{2}},$$ $$\textbf{ 512}$$$$\boldsymbol{\ cm^{3}}$$