The floor area of a tent is in the form of a right circular cone is 3168 by 7 m square. The area of canvas required for the tent is 3960 by 7 m square. Find the air capacity of the tent.
Answers
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
Therefore, the air capacity of the tent is 1357.7 m³
Answer:
Step-by-step explanation:
πr² = 3168/7
22/7 × r² = 3168/7
r² = 3168/22
r² = 288/2
r² = 144
r = 12 m
πrl = 3960
22/7 × 12 × l = 3960
l = 15×7
l = 95 m
l² = r² + h²
95² - 12² = h²
9025 - 144 = h²
8881 = h²
h =94.2396 m
volume of cone = 1/3 × πr²h
= 1/3 ×22/7 × 144 × 94.2396
= 1/3 ×22 × 144 ×13.4628
=22 ×144 ×4.4876
=14216.7168 m³
the air capacity of the tent = 14216.7168 m³
pls accept friend request