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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
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B
75
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C
25
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D
45
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Solution

The correct option is D 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×(edge)2=6×25=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 × breadth + height × length + height × breadth)
S.A. =2(10×5+5×5+5×10)=250 square inch
The difference between the two surface areas is thus 300250=50 square inch.

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