Horse stable is in the form of a cuboid, whose external dimensions are 70 m × 35 m × 40 m, surrounded by a cylinder halved vertically through diameter 35 m and it is open from one rectangular face 70 m × 40 m. Find the cost of painting the exterior of the stable at the rate of Rs 2/m²
Solution:
The horse stable as described above can be represented by the schematic diagram below:
The area which needs to be painted is as follows:
Area to be painted = Back Wall of the stable (1) + Side Walls (2 & 6) of stable + Curved surface of cylindrical roof (5) + Side walls of cylindrical roof(3 & 4)
Let
the radius of the cylindrical roof = r
Height of the cuboid part of the stable = H
Breadth of the stable = b
Length of the stable = l
We know from the diagram above:
r = 35/2 m
H = 40 m
b = 35 m
l = 70m
Area to be painted = l × h + b × h + b × h + (½)(2πrl) + (½)(πr²) + (½)(πr²)
Basically there are six surfaces to be painted:
Area = 70 × 40 + 35 × 40 + 35 × 40 + (½)(2 × 22/7 × 35/2 × 70) + (½)(22/7 × 35/2 × 35/2) +
(½)(22/7 × 35/2 × 35/2)
= 2800 + 1400 + 1400 + 3850 + 1925/4 + 1925/4
= 5600 + 3850 + 962.5
= 5600 + 4812.5
= 10412.5m²
Cost of painting the surface = Rs..2/m²
Total Cost of Painting = 10412.5 × 2 = Rs. 20,825
✦ Try This: Horse stable is in the form of a cuboid, whose external dimensions are 35 m × 28 m × 35 m, surrounded by a cylinder halved vertically through diameter 28 m and it is open from one rectangular face 35 m × 35 m. Find the cost of painting the exterior of the stable at the rate of Rs 3/m²
The horse stable as described above can be represented by the schematic diagram below:
The area which needs to painted is as follows:
Area to be painted = Back Wall of the stable (1) + Side Walls (2 & 6) of stable + Curved surface of cylindrical roof (5) + Side walls of cylindrical roof(3 & 4)
Let
radius of the cylindrical roof = r
Height of the cuboid part of the stable = H
Breadth of the stable = b
Length of the stable = l
We know from the diagram above:
r = 28/2 m = 14m
H = 35 m
b = 28 m
l = 35m
Area to be painted = l × h + b × h + b × h + (½)(2πrl) + (½)(πr²) + (½)(πr²)
Basically there are six surfaces to be painted:
Area = 35 × 35 + 28 × 35 + 28 × 35 + (½)(2 × 22/7 × 28/2 × 35) + (½)(22/7 × 28/2 × 28/2) +
(½)(22/7 × 28/2 × 28/2)
= 1225 + 980 + 980+ 1540+ 308+ 308
= 1225 + 1960+ 1540 + 616
= 1225+ 4116
= 5341m²
Cost of painting the surface = Rs..3/m²
Total Cost of Painting = 5341 × 3 = Rs. 16023
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Sample Problem 11
The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium
Summary:
Horse stable is in the form of a cuboid, whose external dimensions are 70 m × 35 m × 40 m, surrounded by a cylinder halved vertically through diameter 35 m and it is open from one rectangular face 70 m × 40 m. The cost of painting the exterior of the stable at the rate of Rs 2/m² is Rs. 20,825
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