A circus tent is cylindrical to a height of 3 metres and conical above it.If it's diameter is 105m and the slant height of the conical portion is 53m,calcuulate the length of the canvas 2.5m wide to make the required tent.
Answers
Answer:
Step-by-step explanation:
- Height of the cylinder = 3 m
- Diameter = 105 m
- Slant height of the cone = 53 m
- Width of the canvas = 2.5 m
- Length of the canvas
➾ First we have to find the area of canvas required to make the tent.
➾ Given that the tent is in the shape of a cylinder at the bottom.
➾ The curved surface area of the cylinder is given by,
CSA of the cylinder = 2π r h
➾ Substituting the data,
CSA of the cylinder = 2× 3.14 × 105/2 × 3
CSA of the cylinder = 989.1 m²
➾ Now the tent is in the shape of a cone on the top
➾ CSA of a cone is given by,
CSA of the cone = π r l
➾ Substitute the data,
CSA of the cone = 3.14 × 52.5 × 53
CSA of the cone = 8737.05 m²
➾ Hence ,
The area of the canvas = 989.1 + 8737.05
The area of the canvas = 9726.15 m²
➾ Now the area of the canvas is also given by,
Area of canvas = length × breadth
➾ Substitute the value of breadth and area
9726.15 = length × 2.5
Length = 9726.15/2.5
Length = 3890.46
➾ Hence the length of canvas required is 3890.46 m
➾ The CSA of a cylinder is given by,
CSA of the cylinder = 2 π r h
➾ The CSA of a cone is given by,
CSA of a cone = π r l
Answer :-
★ Length of the canvas = 3890.46 m
_____________________
★ Concept :-
Here the concept of Curved Surface area of Cone and Cylinder had been used. According to this, except base of cone and cylinder, the area of left figure is measured.
• CSA of cone = πrl
• CSA of cylinder = 2πrh
Also, here the area of rectangular piece is used.
• Area of Rectangle = Length × Breadth
________________________________
★ Solution :-
Given,
☞ Height of the cylinder, h = 3 m
☞ Diameter of the base, d = 105 m
☞ Radius of the base, r = 105/2 m
☞ Slant height of the cone, l = 53 m
☞ Width of the canvas, b = 2.5 m
» Let the length of the canvas be 'l'. Then,
________________________________
• In order to find the total area of canvas required, we must find out the total curved surface area of the figure. This is given by :-
» Total Area of Canvas = CSA of Cylinder + CSA of cone
________________________________
Now let us calculate the CSA of cylindrical portion. Then,
✒ CSA of Cylinder = 2πrh
✒ CSA of cylinder = 2 × 22/7 × 105/2 × 3
✒ CSA of cylinder = 989.1 m²
________________________________
Now let us calculate the CSA of conical portion. Then,
✒ CSA of Cone = πrl
✒ CSA of Cone = 22/7 × 105/2 × 53
✒ CSA of Cone = 9726.15 m²
________________________________
Now let us calculate the length of canvas. So,
✏ Area of Canvas = Length × Breadth
✏ Area of Canvas = l × b
✏ 9726.15 = l × 2.5
✏
✏ Length = 3890.46 m
✳ Hence, the length of canvas = 3890.46 m
_______________________
★ More to know :-
• CSA of Square = 4 (side) ²
• Volume of cylinder = πr²h
• Volume of cone = ⅓ (πr²h)
• Volume of Cube = (side) ³
• Volume of Cuboid = Length × Breadth × Height