Question : A solid hemisphere has a radius 21 cm. It is melted to form a cylinder such that the ratio of its curved surface area to total surface area is 2 : 5, What is the radius (in cm) of its base (take $\pi=\frac{22}{7}$ )?

Question : A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is melted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes? 

Question : The difference between the length of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. If the area of the trapezium is 1380 cm², then find the length of each of the parallel sides (in cm).

Question : The area of two similar triangles is 324 cm² and 289 cm², respectively. What is the ratio of their corresponding altitudes?

Question : Three cubes of iron whose edges are 6 cm, 8 cm, and 10 cm, respectively, are melted and formed into a single cube. The edge of the cube formed is: