A wooden bookshelf has external dimensions as
follows: Height = 110 cm, Depth = 25 cm,
Breadth = 85 cm (see Fig. 13.31). The thickness of
the plank is 5 cm everywhere. The external faces
are to be polished and the inner faces are to be
painted. If the rate of polishing is 20 paise per
cm and the rate of painting is 10 paise per cm²,
find the total expenses required for polishing and
painting the surface of the bookshelf.
Answers
Answer:
External length (l) of bookshelf=85㎝
External breadth (b) of bookshelf=25㎝
External height (h) of bookshelf=110㎝
External surface area of book shelf while leaving out the front face of the shelf=lh+2(lb+bh)
=(85×110)+2(85×25+25×110)
=9350+9750
=19100㎠
Area if front face=(85×110)−75×100+2(75×5)
=1850+760=2600㎠
Area to be polished=19100+2600=21700㎠
Cost of polishing=Rs. 21700×0.20=Rs.4340
Length, breadth and height of each row of bookshelf are
75㎝,20㎝ & 30㎝ respectively. From the figure Area to be painted in 1 row=2(l+h)b+lh
=2(75+30)20+75×30
=6450㎠
Area to be painted in 3 rows=3×6450=19350㎠
Total cost of painting=Rs.(19350×0.1)=Rs. 1935
Total expenses=Rs.(4340+1935)=Rs. 6275
Step-by-step explanation:
External height (l) of book self = 85 cm External breadth (b) of book self = 25 cm External height (h) of book self = 110 cm 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. 6275Read more on Sarthaks.com - https://www.sarthaks.com/116449/wooden-bookshelf-has-external-dimensions-follows-height-110-depth-breadth-given-figure
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Answer:
External length (l) of bookshelf=85㎝
External breadth (b) of bookshelf=25㎝
External height (h) of bookshelf=110㎝
External surface area of book shelf while leaving out the front face of the shelf=lh+2(lb+bh)
=(85×110)+2(85×25+25×110)
=9350+9750
=19100㎠
Area if front face=(85×110)−75×100+2(75×5)
=1850+760=2600㎠
Area to be polished=19100+2600=21700㎠
Cost of polishing=Rs. 21700×0.20=Rs.4340
Length, breadth and height of each row of bookshelf are
75㎝,20㎝ & 30㎝ respectively. From the figure Area to be painted in 1 row=2(l+h)b+lh
=2(75+30)20+75×30
=6450㎠
Area to be painted in 3 rows=3×6450=19350㎠
Total cost of painting=Rs.(19350×0.1)=Rs. 1935
Total expenses=Rs.
(4340+1935)=Rs. 6275(4340+1935)=Rs.6275
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