From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid. (.…

Diameter of cone \(\displaystyle =14 \mathrm{~cm}\) Radius \(\displaystyle =7 \mathrm{~cm}\) Height of cone \(\displaystyle =14 \mathrm{~cm}\) Slant height \(\displaystyle l=\sqrt{14^{2}+7^{2}}=7 \sqrt{5}=15.4 \mathrm{~cm}\) Volume of remaining solid = Volume of cube - Volume of cone \[\begin{aligned} & =(14)^{3}-\frac{1}{3} \times \frac{22}{7} \times(7)^{2} \times 14 \\ & =\frac{6076}{3} \mathrm{~cm}^{3} \end{aligned} \] Surface area of remaining solid = Surface area of cube - Area of circle + Curved surface area of cone \[\begin{aligned} & =6 \times 14 \times 14-\frac{22}{7} \times 7 \times 7+\frac{22}{7} \times 7 \times 15.4 \\ & =1360.8 \mathrm{~cm}^{2} \end{aligned} \]