A tent is made in such a way that the radius of the base is 1.4m and height us 3.5m and is surmounted by a cone whose radius is same as the radius of a cylindrical part and height is 2.1m find the volume of air in the tent.
Volume of yhe cylindrical part of yhe tent=_______
Volume if the conical part of the tent=_________
Volume of air in the tent =_________
Answers
Given:
A tent is made in such a way that the radius of the base is 1.4m and height us 3.5m and is surmounted by a cone whose radius is same as the radius of a cylindrical part and height is 2.1m
To find:
find the volume of air in the tent.
Solution:
From given, we have,
The radius of the tent = the radius of the cylindrical part = the radius of the conical part = 1.4 m
The height of the tent = 3.5 m
The height of the cylindrical part = 2.1 m
Volume of the cylindrical part of the tent
= πr²h
= π × 1.4² × 2.1
= 4.116π
Volume of the conical part of the tent
= 1/3πr²h
= 1/3 × π × 1.4² × (3.5 - 2.1)
= 0.9146π
Volume of air in the tent = Volume of the cylindrical part + Volume of the conical part
= 4.116π + 0.9146π
= 5.03π
Therefore,
the volume of the cylindrical part = 4.116π = 12.93 m³
the volume of the conical part = 0.9146π = 2.873 m³
the volume of the air in the tent = 5.03π = 15.8 m³