A rectangular block with sides 6 cm, 12 cm and 15 cm is cut up into an exact number of equal cubes. The least possible number of cubes is?

A right circular cylinder has radius 7 cm and height 10 cm. Another cylinder has twice the height and half the radius. The ratio of their volumes (first : second) is:

A cuboidal slab of copper having dimensions 22 cm $\times$ 10 cm $\times$ 5 cm is melted and recasted in the form of a wire of 1 mm diameter. The wire is rubber coated at the rate of Rs. 1.50 per meter. Find the cost of rubber coating (in Rs.) Use $\pi = \frac{22}{7}$.

A sphere of maximum volume is 'cut out' from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut-out sphere is:

64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r.

Which of the following statements are true?

(A) If the diagonal of a cube is $6\sqrt{3}$ cm, then its volume and surface area are equal.

(B) If a rectangular block having dimensions 6 cm x 12 cm x 15 cm is cut into an exact number of equal cubes, then the least possible number of such cubes is 27.

Choose the correct answer from the options given below:

Three solid cubes of sides 1 cm, 6 cm, and 8 cm are melted to form a new cube. The surface area of the cube so formed is: