An open box is made of wood 3 cm thick. Its external length,

Question:

An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface of Rs 50 per sq. metre.

Solution:

Given Data:

Outer Dimensions

Length = 148 cm

Height = 83 cm

Inner Dimensions

Length = 148 - (2 * 3) = 142 cm

Breadth = 116 - (2 * 3) = 110 cm

Height = 83 - 3 = 80

Surface Area of the Inner region = 2h(l + b) + lb

= 2 * 80(142 + 110) + 142 * 110

= 2 * 80 * 252 + 142 * 110

$=55940 \mathrm{~cm}^{2}$

$=5.2904 \mathrm{~m}^{2}$

Hence, the cost of Painting the Surface Area of the Inner region= 5.2904* 50

= Rs. 279.70