Question

two rectangular solid metallic cuboid 12cm 10cm 5cm and 12cm 5cm 4cm are melted together and recast into solid cubes each of side 3cm. how many solid cubes can be made from the metal

Answer 1

l=12cm L=12cm
b=10cm B=5cm
h=5cm H=4cm

Vol of lbh + Vol of LBH=n×Vol of cube
600+240=n×27
840=27n
n=840/27
n=31.1
n=31cubes

Answer 2

Volume of cuboid 1- L x B x H
12x10x5=600cm sqaure

Volume of cuboid 2- 12x5x4=240cm square

Total volume = volume of cuboid 1 + volume of cuboid 2=240+600= 840cm square

Now, volume of square = side cube
So, Number of cubes formed will be total volume upon volume of 1 cube
Volume of 1 cube = side cube = 27cm square
No. Cubes formed = 840/27=31(approx)