Question

The length, breadth and height of a rectangular parallelopiped are in ratio $6:3:1$. If the surface area of a cube is equal to the surface area of this parallelopiped; then what is the ratio of the volume of the cube to the volume of the parallelopiped?

• A. $1:1$
• B. $5:4$
• C. $7:5$
• D. $3:2$

Answer 1

The correct option is D $3:2$

Length: Breadth: Height::$6:3:1$

Let the height of the parallelopiped be $x$.

Thus Length and Breadth are$6x\text{and}3x.$

Surface area of parallelopiped is $2$$(LB+LH+HB)$$=2(6x×3x+6x×x+3x×x)=54x^2.$

Surface area of cube is $6h^2$

Thus $6h^2=54x^2.$

$h^2=9x^2$

$h=3x$

Now ratio of volume

$\frac{\text{volume of cube}}{\text{volume of parallelopiped}}$ $=$ $\frac{h^3}{LBH}$

$\frac{h^3}{6x\times 3x\times 1x}$= $\frac{(3x{)}^3}{18x^3}$ $=$ $\frac{27x^3}{18x^3}$ $=$ $\frac{3}{2}$