Ex.13.5 Q4 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

Q4. Find the cost of digging a cuboidal pit \(8 \rm m\) long, \(6\rm m\) broad and \(3\rm m\) deep at the rate of \(\rm Rs \,30 \,\rm per\)\(\begin{align}\,\rm {m^3} \end{align}\).

Text Solution

Reasoning:

Volume of the pit will be equal to volume of a cuboid and the cost to dug the pit will be equal to product of the volume of the pit and cost to dig the pit per meter cube.

What is known?

The length, breadth and height the cuboid. Cost of digging \(\rm Rs\, 30\, per\)\(\begin{align}\rm {m^3} \end{align}\).

What is unknown?

Cost of digging the cuboidal pit.

Steps:

length\((l) = 8\,\,\rm m\)

breadth\((b) = 6\,\,\rm m\) 

height\((h) = 3\,\,\rm m\) 

Volume of the cuboid \(\begin{align} = l \times b \times h \end{align}\) \(\begin{align} = 8 \times 6 \times 3\,\,\rm {m^3} \end{align}\)

Cost of the digging the pit is \(\rm Rs\, 30 \,per\) \(\begin{align} \rm {m^3} \end{align}\)

\(\therefore\) Cost of digging for \(\begin{align}~\,8\times 6\times 3\,\,\rm {{m}^{3}} \end{align}\)

\[\begin{align} & =30\times 8\times 6\times 3 \\ & =Rs\,\,4320~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \end{align}\]

Answer:

Cost of digging the cuboidal pit is \(\rm= Rs 4320.\)