The floor area of a tent which is in the form of a right circular cone is 3168 by 7 m square.the area of canvas required for making the tent is 3960 by 7 m square.find the air capacity of the tent
Answers
Given: Floor area = 3168 / 7 m^2, area of canvas required for making the tent is 3960 / 7 m
To find: The air capacity of the tent?
Solution:
- Now we have given the area of floor as 3168 / 7 m^2.
- Comparing it with the formula, we get:
3168/7 = πr^2
- As the floor is a circle.
πr^2 = 3168/7
r^2 = 3168/7 x 7/22
r^2 = 144
r = 12
- So the area of canvas will be Lateral Surface Area of a cone
2960/7 = πrl
22/7 x 12 x l = 2960/7
l = 2960/7 x ( 7/22) x 1/12
l = 15
- Now applying Pythagoras Theorem, we get:
h^2 = l^2 - r^2
h^2 = 15 x 15 - 12 x 12
h^2 = 225 - 144
h^2 = 81
h = 9 m
- So now volume of a cone will be:
V = 1/3 x πr²h
V = 1/3 * 22/7 * 144 * 9
V = 1357.7 m^3
Answer:
So the air capacity is 1357.7 m^3
Given:
The floor area of a tent which is in the form of a right circular cone is 3168 by 7 m square. The area of canvas required for making the tent is 3960 by 7 m square.
To find:
Find the air capacity of the tent
Solution:
From given, we have,
Floor area = 3168/7 = πr² (∵ circular floor)
πr² = 3168/7
r² = 3168/7 × 7/22 = 144
r = 12
Area of canvas = 2960/7 = πrl (∵ L.S.A. of a cone)
22/7 × 12 × l = 2960/7
l = 15
using Pythagoras Theorem, we have,
h² = l² - r²
h² = 15² - 12² = 225 - 144 = 81
h = 9
Volume of a cone = 1/3πr²h
= 1/3 × 22/7 × 144 × 9
= 1357.7 m³