the lower part of a circus tent is right circular cylinder and its upper part is a right circular cone the diameter of the base of the tent is 56 M height of the cone is 15 M the total height of the the tent 60 m how many square metres of Canvas is required for the tent? find the volume of the air space in tent
Answers
Answer:
Step-by-step explanation:
Given that the this is a tent , both the cylindrical part and the conical parts are open.
We therefore need the surface area of the curved surfaces of the cone and the cylinder shapes.
The formulas are as follows :
Curved Surface area of a cone = 2πrl
where l = the lateral length of the cone
Curved surface area of a cylinder = 2πrh
where h = the height of the cylinder.
Curved surface area of the cone
We need to find the lateral length.
Given that it is a right cone ,we will use pythagoras theorem to get the length.
the lateral length is the hypotenuse in this case and the radius is the base.
the radius of the cone = 56/2 = 28m
height = 15 m
by pytrhagoras theorem :
l = √(28² + 15²)
l = 31.76m
Area = 2 × 28 × 22/7 × 31.76 = 5589.76m²
Curved Surface area of the cylinder
We need the height of the cylinder
height of the cylinder = total height - height of the cone
= 60 - 15 = 45m
Area = 2 × 28 × 22/7 × 45 = 7920 m²
Total canvas required
7920 + 5589.76 = 13509.76
= 13509.76 m²
Volume of the air space
= volume of the cone + Volume of the cylinder
Volume of a cone = 1/3πr²h
Volume = 1/3 × 22/7 × 28² × 15 = 12320 m³
Volume of the cylinder = πr²h
volume = 22/7 × 28² × 45 = 110880 m³
Total volume = 110880 + 12320 = 123200