Ratios & Proportion

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The total surface area of a solid iron cube and a solid aluminium cuboid are the same. The length, breadth and height of the cuboid are in the ratio $1:2:4$. Both are melted together in a vessel. What is the ratio of iron and aluminium in the resultant mixture?









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Option(A) is correct

\(\begin{align*} 6a^2&=2(lb+bh+hl)\\ l:b:h&=1:2:4\\ \text{ Therefore, } b&=2l,h=4l\\ \text{Hence }6a^2&=2\times (2l^2+8l^2+4l^2)\\ 6a^2&=28l^2\\ a^3&=(14/3)^{3/2}l^3\\ a^3:lbh&=(14/3)^{3/2}:8 \end{align*}\)

(1) Comment(s)

Bhavin Shah

How did 6a rest to 2 come ?

and how did a rest to 3 come?