Question

A cuboid is made of metal. It is 27 cm x 18 cm x 12 cm. It is melted and recast into small cubes with an edge 6 cm in length. How many cubes are made assuming that there is no wastage in the process?

Answer 1

Answer:

GIVEN

The dimensions of the cuboid =  27 cm x 18 cm x 12 cm

cuboid melted into small cubes of side = 6cm

TO FIND

How many small cubes are made.

Assumptions

there is no wastage in the process

SOLUTION

Let, n be the number of cubes formed.

volume of cuboid = n x volume of cube

27 x 18 x 12 = n x 6³

n = $\frac{27 * 18 * 12}{6 * 6 * 6}$

n = 27

27 cubes of side 6 cm are formed in the process. (Ans

VERIFICATION

volume of cuboid = n x volume of cube

LHS :-

volume of cuboid = 27 x 18 x 12

= 5832

RHS :-

volume of 27 cubes = 27 x (6³)

= 5832

LHS = RHS

hence, the answer is correct. :D