Question

The dimensions of a solid metal cuboid are $72cm\times 30cm\times 75cm.$ it is metaled and recast into identical solid metal cubes with edge of each $6$ cm. Find the number of cubes formed.
Also, find the cost of polishing the surface of all the cubes formed at the rate Rs. $150$ per sq. m.

• A. $427$ ; Rs. $2,430$
• B. $830$ ; Rs. $2,430$
• C. $571$ ; Rs. $2,430$
• D. $750$ ; Rs. $2,430$

Answer 1

The correct option is D $750$ ; Rs. $2,430$

Given a solid metal cuboid with dimension $72cm\times 30cm\times 75cm$. It is melted, recast into cube of edge $6$ cm.
For forming cube by melting, we have to find volume of cuboid $=l\times b\times h=72cm\times 30cm\times 75cm=162000{cm}^3$
Volume of the cube to be formed $={\left(side\right)}^3=6^3=216{cm}^3$
So, number of cubes formed $=\frac{\text{Volume of cuboid}}{\text{Volume of cube}}$ $=\frac{162000}{216}=750$

For polishing the cube we need to find total surface area of cube.
Total surface area of one cube $=6\times {\left(side\right)}^2=6\times 6^2=216{cm}^2$

Total surface area of the $750$ cubes $=216{cm}^2\times 750=162000{cm}^2=16.2m^2$

Cost of polishing per sq.m is Rs. $150$.
Therefore, cost of polishing 16.2 sq m $=16.2m^2\times 150=Rs.2430$