Question

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

Answer 1

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

Answer 2

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