3. Example problem of cuboid

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 \(m^2\).

 

 

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 \(₹1350\).