Square-based box from surface and diagonal

Text

A rectangular box has a square base of edge $6$ cm and height $7$ cm. Find the total surface area, the space diagonal and the volume.

Solution

Total surface: $S=2\cdot6^2+4\cdot(6\cdot7)=72+168=240$ cm$^2$. Space diagonal: $d=\sqrt{6^2+6^2+7^2}=\sqrt{36+36+49}=\sqrt{121}=11$ cm. Volume: $V=6\cdot6\cdot7=252$ cm$^3$. $\boxed{S=240\ \text{cm}^2;\ d=11\ \text{cm};\ V=252\ \text{cm}^3}$