Question

10 cubic metres clay is uniformly spread on a land of area 10 acres, what is the rise in the level of the ground?
A. 1cm
B. 10cm
C. 100cm
D. 1000cm

Answer 1

Hint: Volume can be written as Area times height which gives height=Volume/Area. Using the given area and volume in the question find the rise (height) of the ground.
1 are=100 square meters.


Complete step-by-step Solution:
We are given that the Volume of the clay is 10 cubic metres and area of the land is 10 ares.
We have to find the rise in the level of the ground after uniformly spreading the clay on the land.
$
  1are = 100{m^2} \\
  10ares = 10 \times 100{m^2} \\
  10ares = 1000{m^2} \\
 $
Area of the land is 1000 square metres.
Volume of the clay is 10 cubic metres.
Volume=Area × height
Height=Volume/Area
$
  h = \dfrac{V}{A} \\
  h = \dfrac{{10{m^3}}}{{1000{m^2}}} \\
  h = \dfrac{1}{{100}}m \\
  1m = 100cm \\
  1cm = \dfrac{1}{{100}}m \\
  \therefore h = 1cm \\
 $
When the clay of volume 10 cubic metres is uniformly spread on a land of 10 ares then the rise of the level of the ground is 1cm.
Therefore, from among the option A in the question option A is correct which is 1cm.


Note: Many people might not know about are. The original French metric system had a unit of land area, the ‘are’, which was 10 m x 10 m or 100 square metres. So ‘are’ is used as a measurement of land.