Question

The Length breadth and Height of a cuboid are in the ratio 3:2:1.Its Volume is 384 cm cube.find the total surface area of the cuboid

Answer 1

volume = l × b × h
384 = 3x × 2x × 1x
384 = 6x³
384/6 = x³
64 = x³
x = 4

l = 12cm , b = 8cm, h 4cm

TSA = 2(lb + bh + hl)
TSA = 2(96 + 32 + 48)
TSA = 2(176)

TSA = 352cm²

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Answer 2

Total Surface Area of Cuboid is 352 $cm^2$

Step-by-step explanation:

If the length, breadth and height are in the ratio 3:2:1 then the dimensions are 3x, 2x and x for some value of x. Therefore, in terms of x, the volume = $(3x) \times (2x) \times x = 6x^3$.

So $6x^3 = 384$

$x^3 = 64$

x = 4

The dimensions of the box are $(3 \times 4), (2 \times 4), 4$

i.e. 12, 8 and 4 cm.

Therefore its surface area =

$2[(12 \times 8) + (12 \times 4) + (8 \times 4)]$

= 2(96 + 48 + 32)

= 352 $cm^2$