The dimensions of a cuboid are in ratio 4:3:2. If the total surface area of the cuboid is 4212 square metres. Find the volume of the cuboid.

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17685cm³

67455cm³

17496cm³

25764cm³

answer is C.

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Detailed Solution

Express length, breadth and height in terms of k.
As it is given in the question that length, breadth and height are in the ratio of 4:3:2
Length = 4k.........(1)
Breadth = 3k........(2)
Height = 2k........(3)

Since, total surface area of a Cuboid
= 2(lb+bh+hl)

Total Surface area given in the question
= 4212m²

Equating both the values
2(lb+bh+hl)=4212m²

From (1), (2), and (3) we have
2(4k×3k+3k×2k+2k×4k)=4212m²

⇒2(12k²+6k²+8k²)=4212m²

⇒52k²=4212m²

⇒k²=81
Taking square root on both sides,

\sqrt{k 2} = \sqrt{81}

k = \sqrt{9^{2}}

k = 9

Substitute the value of k=9 in length, breadth, and height.
Length l=4k=4(9)=36m … (4)
Breadth                                                        b=3k=3(9)=27m ... (5)
Height h=2k=2(9)=18m ... (6)
Now we find the volume by substituting the values inthe formula.
We know volume .                                                    =l×b×h
                                 =36×27×18
                                 =17496m³

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