A tent is made in form of a conic frustum cermounted by a cone .The diameter of base and top of the frustum are 20m and 6m respectively and height 24m. If height of tent is 28meters find the quantity of canvas required and the amount of air present in the tent

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Asked: 2023-11-02T16:19:28+05:30 In: Mathematics
A tent is made in form of a conic frustum cermounted by a cone .The diameter of base and top of the frustum are 20m and 6m respectively and height 24m. If height of tent is 28meters find the quantity of canvas required and the amount of air present in the tent

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    2. For the lower portion of the tent:

      Diameter of the base = 20 m

      Radius, R, of the base = 10 m

      Diameter of the top end of the frustum = 6 m

      Radius of the top end of the frustum = r = 3 m

      Height of the frustum = h = 24 m

      Slant height = l

      =√h2+(R−r)2=√242+(10−3)2=√576+49=√625=25 m

      For the conical part:

      Radius of the cone= base = r = 3 cm

      Height of the cone = Total height – Height of the frustum = 28 – 24 = 4 m

      Slant height, L, of the cone =√32+42=√9+16=√25=5 m

      Total quantity of canvas = Curved surface area of the frustum + Curved surface area of the conical top

      =(πl(R+r))+πLr=π(l(R+r)+Lr)=227(25×13+5×3)=227(325+15)=1068.57 m2

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