Question

Two rectangular solid metallic cuboids $12cm\times 10cm\times 5cm$ and $12cm\times 5cm\times 4cm$ are melted together and recast into solid cubes each of side $2cm$. How many solid cubes can be made from the metal?

• A. $105$
• B. $100$
• C. $96$
• D. $80$

Answer 1

The correct option is A $105$

Number of cubes formed $=\frac{\text{Volume of cylinder 1 + Volume of cylinder 2}}{\text{Volume of one cube}}$
Volume of a cube of edge $a=a^3$
Volume of a cuboid of length $l$, breadth $b$ and height $h$ $=l\times b\times h$.
Hence, number of cubes formed $=\frac{(12\times 10\times 5)+(12\times 5\times 4)}{2\times 2\times 2}=105$