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
Breadth = 116 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
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