Question

If two cubes of equal volume are to be made from rectangular block of volume $250$ cubic inches, then the combined surface area of the two cubes is greater than the surface area of the original rectangular block by $x$ square inches. Find the value of $x$.

• A. $50$
• B. $75$
• C. $25$
• D. $45$

Answer 1

Answer: (A)

$50$

Two cubes are to be made from a rectangular block of volume $250$ cubic inch.

This implies that the volume of each cube would be $125$ cubic inch.

Thus, the edge of each cube would be $5$ inch.

Surface area of one cube $=6\times (edge{)}^2=6\times 25=150$ square inch

Surface area of $2$ cubes becomes $300$ square inch.

When joined together, the two become a cuboid of length $10$ inch, breadth $5$ inch and height $5$ inch.

The surface area of the cuboid can be found out as

S.A. $=2$ (length $\times$ breadth + height $\times$ length + height $\times$ breadth)

$\therefore$ S.A. $=2(10\times 5+5\times 5+5\times 10)=250$ square inch

The difference between the two surface areas is thus $300-250=50$ square inch.