In a marriage ceremony of her daughter, Manita. Rakesh has to make arrangements for the
accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way
that each person has 4 sq. metres of the space on ground and 20 cubic metres of air to breathe.
What should be the height of the conical tent?
Answers
The height of the conical tent is 15 metres.
• Given data :
Total number of people in the tent is 150.
Area required for one person is 4 square metre.
Air required for one person is 20 metre cube.
• At first we have to calculate the area of the base of the tent by using the following mathematical formula :
= Total number of people × Area required for one person
= 150 × 4
= 600 m²
• Now, we have to calculate the area of the tent by using the following mathematical formula :
= Total number of people × Volume of air necessary for one people
= 150 × 20
= 3000 m³
• Let the radius of the base = r metres ( assume r as a variable to calculate the radius of the base)
• Area of the base = πr²
• So,
πr² = 600
r² = 600/π
• Let,the height of the tent = h metres ( assume h as a variable)
•Now,the volume of the tent
= 1/3 × π × r² × h
= 1/3 × π × 600/π × h
= 200h
Now,two values battery calculated about the volume of the tent,then we will get the following equation :
200h = 3000
h = 15
So,the height of the tent is 15 metres. (Answer)