Question

The ratio of the base area and the curved
surface area of a conical tent is 40 : 41. If its
height is 18m, find the air capacity of the tent in
terms of pi.​

Answer 1

Step-by-step explanation:

Given  

The ratio of the base area and the curved surface area of a conical tent is 40 : 41. If its height is 18 m,

 Given ratio is 40 : 41

So base area / curved surface = 40 / 41  

     So π r^2 / π r √ h^2 + r^2 = 40 / 41 (where h is height and r is radius of conical tent)

  Now r / √ 18^2 + r^2 = 40 / 41 (since h = 18 m)

       Squaring both sides we get

             r ^2 / 18 + r^2 = 1600 / 1681

       1681 r^2 = 1600 (18^2 + r^2)

        1681 / 1600 r^2 = 324 + r^2

           1.050625 r^2 – r^2 = 324

         So r^2 = 324 / 0.050625

            So r^2 = 6400

                 Or r = 80 m

Now air capacity = 1/3 π r ^2 h

                          = 1/3 π x 80 x 80 x 18

                         = 38, 400 π cu m