Question

A closed tank has internal size of \[10\;m \times 15\;m \times 20\;m\]. It needs to be lined with waterproofing cement on all its internal sides. At the rate of Rs. \[250\] per $ {m^2} $ , the total cost of lining will be Rs.
(A) \[237,500\]
(B) \[325,000\]
(C) \[400,000\]
(D) \[475,000\]

Answer 1

Hint: First calculate the area of the closed tank with the help of the formula for the area of the cuboid and then multiply the area by the rate of lining per meter square for the cost of the lining of the internal sides.

Complete step-by-step answer:
A closed tank has an internal size of \[10\;m \times 15\;m \times 20\;m\]. It needs to be lined with waterproofing cement on all its internal sides.

When we are solving this type of question, we need to follow the steps provided in the hint part above.
length of tank = (l) = \[10\;m\]
breadth of tank = (b) = \[15\;m\]
height of tank = (h) = \[25\;m\]
shape of tank is as cuboid
so total area of cuboid is given by
$ A= 2[(l\times b) + (l\times h) + (b\times h)] $
\[
\Rightarrow {A{\text{ }} = {\text{ }}2\left[ {150{\text{ }} + {\text{ }}300{\text{ }} + {\text{ }}200} \right]} \\
\Rightarrow A{\text{ }} = {\text{ }}2\left[ {650} \right] \\
\Rightarrow A = 1300\;{m^2} \;
\]
As rate of lining is given as Rs.\[250\] per m2
So total cost of lining as total area to be lined it =\[\;1300\]
\[
  {Total{\text{ }}cost{\text{ }} = {\text{ }}total{\text{ }}area{\text{ }} \times {\text{ }}rate{\text{ }}of{\text{ }}lining} \\
  {\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = {\text{ }}1300{\text{ }} \times {\text{ }}250} \\
  {\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = {\text{ }}325000}
\]
Hence total lining cost would be \[325000\] rupees.
So, the correct answer is “Option B”.

Note: First thing is to remind the formula for the area of the cuboid. Then take care of the calculations needed to calculate the rate of the lining of the cuboid. Also check the units of the area with the rate units.