Question

Three rectangular solid metallic cuboids $20cm\times 10cm\times 5cm,12cm\times 10cm\times 4cm$ and $15cm\times 12cm\times 5cm$ are melted together and recast into solid cubes each of side $5cm$. How many solid cubes can be made from the metal?

• A. $80$
• B. $65$
• C. $52$
• D. $19$

Answer 1

The correct option is D $19$

Number of cubes formed $=\frac{\text{Volume of cylinder 1 + Volume of cylinder 2 + Volume of cylinder 3}}{\text{Volume of one cube}}$
Volume of a cube of edge $a=a^3$
Volume of a cuboid $=l\times b\times h$
Hence, number of cubes formed $=\frac{(20\times 10\times 5)+(12\times 10\times 4)+(15\times 12\times 5)}{5\times 5\times 5}=19.04$
Hence, $19$ complete cubes can be made.