a horse stable is in the form of a cuboid , whose external dimensions are 70m * 35 m * 40m, surrounded by a cylinder halved vertically throught diameter 35m and it is open from one rectangular face 70m by 40m . find the cost of painting the exterior of the stable at the rate of ruppes 4 per m2 . also , verify your answer
Answers
Given : a horse stable is in the form of a cuboid , whose external dimensions are 70m * 35 m * 40m,
surrounded by a cylinder halved vertically through diameter 35m
open from one rectangular face 70m by 40m .
To find : the cost of painting the exterior of the stable at the rate of rupees 4 per m²
Solution:
Cuboid Shape outer Surface area = 2(l + b)h
l = 70
b = 35
h = 40
= 2(70 + 35) * 40
= 8400 m²
one rectangular face = 70 * 40 = 2800 m²
8400 - 2800 = 5600 m²
Top area = (1/2)2πrh = πrh
r = 35/2 m
h = 70 m
π = 22/7
(22/7)(35/2)*70
= 3850 m²
Total area to be painted = 5600 + 3850
= 9,450 m²
cost of painting the exterior of the stable = 9,450 x 4
= 37800 Rs
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Answer:
Step-by-step explanation:
Area of cylindrical top be painted
= 1/2 [T.S.A]
=1/2 [2πR (R + H)]
=1/2[2*22/7*35/2(35/2+70]
= 4812.5 m2
• Area of cuboid to be painted = area of three walls
= lh + 2bh
= 70 × 40 +2 × 40 × 35
= 2800 + 2800
= 5600 sq.m
• Total area to be painted
= 4812.5 + 5600
= 10412.5 sq.m
• Cost of painting per sq.m = Rs 4
Cost of painting 10412.5 sq.m = Rs 10412.5 × 4
= Rs 41650
Area to be painted
= Area of three walls + Area of cylindrical part.
= 2bh + lh + 1 /2 [2πRH + 2πR2]
= h [2b + l ] + [πR (R + H)]
= 40 [2 × 35 + 70] + 22/7*35/2[35/2 +70]
= 40 [140] + 55 × 87.5
= 5600 + 4812.5
= 10412.5 sq.m
Cost of painting 10412.5 sq.m = Rs 10412.5 × 4
= Rs 41650
Final cost (same as in previous method)
Hence verified.