# Find the cost of digging a cuboidal pit $8m$ long, $6m$ broad and $3m$ deep at the rate of $30$ per ${m^2}$.

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Hint: A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces. When the area of the faces of a cuboid is the same, we call this cuboid a cube. The area of all the faces of a cube is the same as they are all squares.
Volume of cuboid: The total surface area of a cuboid is equal to the sum of the areas of the six rectangular faces whereas the Lateral surface area of a cuboid equal to the sum of the four rectangular faces, in which two rectangular faces of the top and bottom faces are excluded.
Since cost is in $30m$. Therefore, Volume of cuboidal pit dug is directly proportional to cost.
Volume of Cuboid $= length \times breadth \times height$

Length of Cuboid $= 8m$
Breadth of Cuboid $= 6m$
Height of Cuboid $= 3m$
According to the Volume of Cuboid Pi $+$
$= length \times breadth \times height$
$= 8 \times 6 \times 3$
$= 144$${m^3}$
Cost of digging cuboidal pit for $1{m^3}$$= \,Rs.30 Cost of digging cuboidal pit 144{m^3}$$ = Rs.(144 \times 30)$
$= Rs.4320$
$\therefore$ Total Cost of digging the pit $= Rs.4320$

Note: Since the cost is in ${m^3}$. So, there will be no alternative. But if there was a cost in ${m^2}$ then the formulae of Total Surface Area will be Applied as.
$T.S.A = 2(length \times breadth + breadth \times height + height \times length)$
And then T.S.A is multiplied with the cost to yet the total cost of digging the cuboidal pit.