[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-
• The circus tent is composed of cylinder and a cone.
• The height and diameter of the cylindrical part are 7m and 10m
• The total height of the circus tent 19m
• The cost of making the tent at a cost of 35 m² cloth.
Let's Begin :-
Here, we have ,
- Cylinder and cone
- The height and diameter of the cylinder are 7m and 10m
- Therefore , radius = 5 m
We know that,
Curved Surface area of the cylinder
[tex]\sf{ = 2{\pi}rh}[/tex]
Subsitute the required values,
[tex]\sf{ = 2{\times}3.14{\times}5{\times}7}[/tex]
[tex]\sf{ = 6.28 {\times}5{\times}7}[/tex]
[tex]\sf{ = 6.28 {\times}35}[/tex]
[tex]\bold{ = 219.8m^{2}}[/tex]
Thus, The area of the cylinder is 219.8m² .
Now,
•We have to find the area of the cone.
•Here, Base of cone = diameter of the cylinder.
•The height of the cone will be
= Height of the tent - Height of cylinder
[tex]\sf{ = 19 - 7 }[/tex]
[tex]\bold{ = 12 m }[/tex]
We know that,
Area of cone
[tex]\bold{ = {\pi}rl }[/tex]
- Here, l is the slant height.
Slant height of the cone
[tex]\sf{ = \sqrt{ h^{2} + r^{2}} }[/tex]
[tex]\sf{ = \sqrt{ (12)^{2} + (5)^{2}} }[/tex]
[tex]\sf{ = \sqrt{ 144 + 25}}[/tex]
[tex]\sf{ = \sqrt{ 169}}[/tex]
[tex]\sf{ = \sqrt{ 13{\times} 13 }}[/tex]
[tex]\bold{ = 13 m }[/tex]
Thus, The slant height of the cone is 13 m
Subsitute the required values in the above formula
[tex]\sf{ = 3.14 {\times} 5 {\times} 13}[/tex]
[tex]\sf{ = 3.14 {\times} 65}[/tex]
[tex]\bold{ = 204.1 m^{2}}[/tex]
Thus, The area of the cone is 204.1 m² .
Therefore ,
The total area of the circus tent
[tex]\sf{ = 204.1 + 219.8}[/tex]
[tex]\bold{ = 423.9m^{2} \: or \: 424 m^{2}}[/tex]
Now,
- We have to find the total cost of making the tent.
- The cost for 1 m² = 35
Therefore,
The total cost for making the circus tent
[tex]\sf{ = 424 {\times} 35}[/tex]
[tex]\bold{ = 14840}[/tex]
Hence, The total cost for making the tent is 14840 .
