Question

A rectangular block 6cm by 12cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

Answer 1

Volume of the block = (6 x 12 x 15) cu.cm = 1080 cu.cm  

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm  

                                  = 3 cm.

Volume of this cube  = (3 x 3 x 3) cu.cm = 27 cu.cm

Number of cubes =1080/27 = 40.

Answer 2

Step-by-step explanation:

Few steps to be noted

✓ Take HCF for the dimensions of rectangle sos as to find the dimension of square.

✓ The formula used to find the number of small cubes has cutted from rectangle is

Vol of rectangle = n×Vol of cube