Question

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

• A. $710$; Rs.$2,430$
• B. $790$; Rs. $2,430$
• C. $740$; Rs.$2,430$
• D. $750$; Rs. $2,430$

Answer 1

Answer: (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 cube to be formed$={\left(side\right)}^3=6^3=216{cm}^3$
So,Number of cubes formed$=\frac{volumeofcuboid}{volumeofcube}=\frac{162000{cm}^3}{216{cm}^3}=750$
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.$=16.2m^2\times 150=Rs.2430$