Theory:

A closed wooden box is in the form of a cuboid. Its length, breadth and height are \(5 \ m\), \(3 \ m\) and \(150 \ cm\) respectively. Find the total surface area and the cost of painting its entire outer surface at the rate of \(₹25\) per \(m^2\).
 
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Solution:
 
Length of the box \(=\) \(5 \ m\)
 
Breadth of the box \(=\) \(3 \ m\)
 
Height of the box \(=\) \(150 \ cm\) \(=\) \(\frac{150}{100}\) \(=\)\(1.5 \ m\)
 
Total surface area \(=\) \(2 (lb + bh + lh)\)
 
\(=\) \(2 ((5 \times 3) + (3 \times 1.5) + (5 \times 1.5))\)
 
\(=\) \(2 (15 + 4.5 + 7.5)\)
 
\(=\) \(2 (27)\)
 
\(=\) \(54 \ m^2\)
 
Total surface area of the box is \(54 \ m^2\).
 
Cost of painting per \(m^2\) \(=\) \(₹25\)
 
Cost of painting for \(54 \ m^2\):
 
\(=\) \(54 \times 25\)
 
\(=\) \(1350\)
 
Cost of painting the entire outer surface area of the box is \(₹1350\).
 
Important!
The units of length, breadth and height should be the same while calculating surface area of the cuboid.