The upper portion of the greenhouse shown in figure-40 is
semicircular. This greenhouse is made up of cloth. It has a wooden
door of size 1.2 m. * 0.5 m. Find the area of the cloth required to
cover the green house completely.
Answers
The area of the cloth required to cover the greenhouse completely is 85 m^2.
Step-by-step explanation:
In order to find the area of the cloth required for covering the complete greenhouse, we can see from the figure given that the lower portion of the greenhouse is the cuboid and the upper portion is half of a cylinder.
Step 1: Area of the cuboidal lower portion of the greenhouse
Length of the cuboid, l = 5 m
Breadth of the cuboid, b = 3
Height of the cuboid, h = 2.5 m
Now,
Area of the cuboidal portion (including door)
= [Area of the 4 walls of the cuboid] + [Area of the floor]
= [2h(l+b)] + [l * b]
= [2 * 2.5(5+3)] + [5 * 3]
= 55 m²
Length of the door is given as = 1.2 m
Breadth of the door is given as = 0.5 m
Therefore,
Area of the cuboidal lower portion of the greenhouse excluding the door, that the cloth will cover is given by,
= [Area of the cuboidal portion(including door)] – [area of the door]
= 55 – [1.2 * 0.5]
= 54.4 m²
Step 2: Area of the half-cylindrical upper portion of the greenhouse
From the figure, we can say,
Diameter of the semicircle = 3 m
∴ Radius of the semicircle, r = d/2 = 3/2 m
Height of the cylinder, h = 5 m
Therefore,
Area of the half-cylindrical upper portion of the greenhouse is given as,
= ½ * [Area of cylinder]
= ½ * [2πr² + 2πrh]
= ½ * 2 * (22/7) * [9/4 + 15/2]
= 22/7 * 39/4
= 30.64 m²
Step 3:
Thus,
The total area of the cloth required to cover the greenhouse completely is given by,
= [Area of the cuboidal lower portion of the greenhouse excluding the door] + [Area of the half-cylindrical upper portion of the greenhouse]
= 54.4 + 30.64
= 85.04
≈ 85 m²
Hope this is helpful!!!!!