Answer

Verified

404.4k+ views

**Hint:**First we will define what is meant by cuboid then we will assume a variable for the length breadth and the height of the cuboid and then we will apply the formula for the total surface area of a cuboid that is $2\left( lb+bh+hl \right)$ then we will get the dimensions of the cuboid. Then for finding the volume of the cuboid we will apply the formula: $\left( length\times breadth\times height \right)$and get the answer.

**Complete step by step answer:**

Let’s first see what is meant by a cuboid. So, A cuboid is a three dimensional shape having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.

Now let the length, breadth and height of the cuboid be $4x,3x\text{ and }2x$.

Given that the surface area of the cuboid is $4212\text{ }{{\text{m}}^{\text{2}}}$.

We know that the surface area of a cuboid of length $l$ , breadth $b$ and height $h$ is $2\left( lb+bh+hl \right)$

Now, we will put the values given in the question to find out the surface area of cuboid:

$\begin{align}

& \Rightarrow 4212=2\left( \left( 4x.3x \right)+\left( 3x.2x \right)+\left( 2x.4x \right) \right) \\

& \Rightarrow 2106=\left( 12{{x}^{2}}+6{{x}^{2}}+8{{x}^{2}} \right) \\

& \Rightarrow 2106=26{{x}^{2}} \\

& \Rightarrow {{x}^{2}}=81 \\

\end{align}$

Taking square roots on both the sides, we will get: $\Rightarrow x=\pm 9$ , since dimension cannot be negative therefore: $x=9$

Now, the length of the cuboid will be $4x=4\times 9=36\text{ m}$ , breadth will be $3x=3\times 9=27\text{ m}$ and height $2x=2\times 9=18\text{ m}$

Now, we know that the volume of the cuboid is $\left( length\times breadth\times height \right)$

Therefore, the volume of the given cuboid will be: $\left( 36\times 27\times 18 \right)=17496\text{ }{{\text{m}}^{3}}$

**Hence, the answer is $17496\text{ }{{\text{m}}^{3}}$ .**

**Note:**Common mistake can be made while applying the total surface area formula and instead of that one can use the lateral surface area formula that is $2h\left( l+b \right)$, this will lead to a totally different answer. Also, units must be mentioned at every step.

Recently Updated Pages

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

How do you find the critical points of yx2sin x on class 12 maths CBSE

How do you find the general solution to dfracdydx class 12 maths CBSE

Trending doubts

The provincial president of the constituent assembly class 11 social science CBSE

Gersoppa waterfall is located in AGuyana BUganda C class 9 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The hundru falls is in A Chota Nagpur Plateau B Calcutta class 8 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE