A children's tent house has a cylindrical wall with a conical ceiling. The height of the cylindrical wall is 5 metres. The floor area covered by the tent is 120 sq. metres and the volume of the tent is 750 cubic metres. Calculate the total height of this tent.
Answers
since tge base is cylindrical the base is circular in shap
area of circle=πr²
floor area is given as 120 m²
»πr² =120
total height of tent= height of cylinder(h)+height of cone(h')
total volume=volume of cylinder + volume of cone
750m³=πr²h + 1/3πr²h'
750=πr²(h+1/3h')
750=120(h+1/3h')
h+1/3h'=6.25
ht of cylinder given as 5m
5+1/3h'=6.25
1/3h'=1.25
h'=3.75m
total height of tent =5+3.75=8.75m
Answer:
Radius of the conical part = radius of cylindrical part r=
2
3
m
Slant height of the cone l=2.8 m
Height of the cylinder, h=2.1 m
Canvas needed to make the tent = Curved surface area of the conical part + curved surface area of the cylindrical part.
Curved surface area of conical part = πrl=
7
22
×
2
3
×2.8=13.2
Curved surface area of cylindrical part =2πrh=2×
7
22
×
2
3
×2.1=19.8
Total surface area = Curved surface area of conical part + Curved surface area of cylindrical part
=13.2+19.8=33 m
2
Cost of 1 m
2
canvas = Rs. 500
Cost of 33 m
2
canvas =33×500=16500
Therefore, it will cost Rs. 16500 for making such a tent.