Question

A pit is dug 50 m long, 40 m broad and 7 m deep. The earth dug out is spread evenly on a plot of land 500 m × 400 m. The level of the plot rises by
A. 0.56 m
B. 0.07 m
C. 0.25 m
D. 0.36 m

Answer 1

Hint:
A cuboid is a three-dimensional shape having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. In cuboids all the angles are at right angles. The three dimensions of cuboid are length, breadth and height.
The volume of a three dimensional shape cuboid, is equal to the amount of space occupied by the shape. The volume of cuboid is given by the product of its dimensions.
Volume of the cuboid = (Length × Breadth × Height)
In this question, the volume of the pit which is dug is equal to the volume of earth taken out to spread it over a plot of land.

Complete step by step solution:
 The volume of earth spread over the plot is equal to the volume of earth taken out of the pit.
Volume of the earth taken out = ${V_1} = L \times B \times H$
Length of the pit = 50 m
Breadth of the pit = 40 m
Height of the pit = 7 m
$\begin{gathered}
  {V_1} = 50 \times 40 \times 7 \\
  {V_1} = 14000{m^3} \ldots \left( 1 \right) \\
\end{gathered} $
Let ‘h’ be the height of the rise in the level of the plot.
Volume of earth spread over the plot= ${V_2}$
${V_2} = 500 \times 400 \times h \ldots \left( 2 \right)$
 On equating equation (1) and (2), we get
\[\begin{gathered}
  {V_1} = {V_2} \\
  50 \times 40 \times 7 = 500 \times 400 \times h \\
  h = \dfrac{{50 \times 40 \times 7}}{{500 \times 400}} \\
  h = \dfrac{7}{{100}} \\
  h = 0.07m \\
\end{gathered} \]
Therefore, the level of the plot rises by 0.07m.
∴Option (B) is correct

Note: The volume of the cuboid is equal to the product of the area of one surface and height. So, in this question, we can also solve it by finding the area of the plot and then we can find the height as the volume is the product of the area and height.