List of top Quantitative Aptitude Questions on Mensuration - Surface Area and Volume

Two solid pyramids are melted together. These pyramids had a number of edges equal to the length of each of their edges, both equal to 8 units. They are moulded to form a hexagonal pyramid with the length of each side of the base equal to 8 units. What is the slant height of the new pyramid?
The figure below is a regular hexagon ABCDEF with side '2a' cm, where AB and DE are its two vertical sides. A rectangle is drawn using AB as one side, with its other two (unlabelled) corners G (on the same level as B) and H (on the same level as A), where AG = FG and ED \( \parallel \) GH. What is the area of the shaded region (the region between the rectangle and the hexagon's boundary)?
A solid metallic cuboid with sides in the ratio 3 : 4 : 6 is melted to form smaller cubes with sides 2 cm. If the sum of the length of the edges of the cuboid is 208 cm, then what is the ratio of the surface area of the original cuboid to the total surface area of the smaller cubes?