A wooden bookshelf has external dimensions as follows: height = 110 cm, depth = 25, breath=85 cm. The thickness of the lpank 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 square, and the rate of painting 10 paise per cm square , find the total expenses required for polishing and painting the surface of the bookshelf.
Please solve it I am facing problem with this sum
Answers
Answer:
Step-by-step explanation:
A book shelf is not a closed cuboid.
It is open on both ends.
The inner dimension of the shelf is :
Height = 110 - 10 = 100 cm
Width = 25 - 10 = 15cm
Length = 85 - 10 = 75 cm
Outer area :
2 × 85 × 110 = 18700 cm sq
2 × 25 × 110 = 5500 cm sq
Total area = 18700 + 5500 = 24200 cm sq
Inner area :
2 × 100 × 15 = 3000 cm sq
2 × 100 × 75 = 15000 cm sq
15000 + 3000 = 18000 cm sq
Amount required for polishing = 20 × 24200 = 484000 paise.
Amount required for painting = 10 × 18000 = 180000
Total :
180000 + 484000 = 664000 paise.
Answer:
The total expenses is Rs 6275
Step-by-step explanation:
Area of the bookshelf to be polished = Area of the five complete surfaces + Area of 2 rectangles of rectangles of dimensions 110 cm * 5 cm in the front + Area of 4 rectangles of dimensions 75 cm * 5 cm in the front
= (110*85+2*85*25+2*110*25+2*110*5+4*75*5)
= 9350+4250+5500+1100+1500
=
∴ Total cost of polishing excluding the thickness of the plank = 110-4*5
= 90 cm
∴ Area to be painted = Area of 3 open cuboids of dimensions
= (75*30*20) cm
= 3*[75*30+2*30*20+2*20*75]
= 3(2250+1200+3000)
=
∴ Total cost of painting = Rs 10/100 * 19350
= Rs 1935
Now
Total expenses required = Rs (4340 + 1935)
= Rs 6275
Hence the expenses required for polishing and painting the surface of the bookshelf is Rs 6275
Hope it helps you
