Wooden book shelf has extended dimensions …
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Wooden book shelf has extended dimensions as follows hight 110cm, depth 25cm, breadth 85cm
The Hickman's of the plank is 5cm every where
The external faces are to be polished and the inner faces are to be painted
If the rate of polishing is 20 paisa/cm square
Find the total expenses required for polishing and panting the surface of the book shelf
Posted by Akshad Tambe 8 years, 10 months ago
- 1 answers
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Naveen Sharma 8 years, 10 months ago
Ans.
External faces to be polished
= Area of six faces of cuboidal bookshelf – 3 (Area of open portion ABCD)
= 2 (110 x 25 + 25 x 85 + 85 x 110) – 3 (75 x 30)
[AB = 85 – 5 – 5 = 75 cm and AD = (1/3 x 110) – 5 – 5 – 5 – 5 = 30 cm]
= 2 (2750 + 2125 + 9350) – 3 x 2250
= 2 x 14225 – 6750
= 28450 – 6750
= 21700 cm2
Now, cost of painting outer faces of wodden bookshelf at the rate of 20 paise.
= Rs. 0.20 per cm2 = Rs. 0.20 x 21700 = Rs. 4340
Here, three equal five sides inner faces.
Therefore total surface area
= 3 [ 2 (30 + 75) 20 + 30 x 75] [Depth = 25 – 5 = 20 cm]
= 3 [ 2 x 105 x 20 + 2250] = 3 [ 4200 + 2250]
= 3 x 6450 = 19350 cm2
Now, cost of painting inner faces at the rate of 10 paise i.e. Rs. 0.10 per cm2.
= Rs. 0.10 x 19350 = Rs. 1935
Total expenses required = Rs. 4340 + Rs. 1935 = Rs. 6275
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