The length, width and height of a rectangular solid are in the ra…

MCQ

The length, width and height of a rectangular solid are in the ratio of $3 : 2 : 1$. If the volume of the box is $48cm^3$, the total surface area of the box is:

A
$27cm^2$
B
$32cm^3$
C
$44cm^3$
✓
$88cm^3$

✓

Answer

Correct option: D.

$88cm^3$

$88cm^3$
Length (l), width (b) and height (h) of the rectangular solid are in the ratio $3 : 2 : 1.$
So, we can take,
$(l) = 3x cm$
$(b) = 2x cm$
$(h) = x cm$
We need to find the total surface area of the box
Volume of the box,
$V = 48cm^3$
$lbh = 48$
$(3x)(2x)x = 48$
$6x^3 = 48$
$x^3 = 8$
$x = 2$
Thus,
Surface area of the box,
$= 2(lb + bh + hl)$
$= 2[(3x)(2x) + (2x)x + (x)(3x)]$
$= 2(11x^2)$
$= 22x^2$
$= 22(2)^2$
$= 88cm^2$
Thus total surface area of the box is $88cm^2.$
Hence, the correct option is (d).

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