area of cone

Question

In an " Arts and Crafts Function" a conical structure with four open doors was built. The slanting height and the base diameter of the conical structure was 22m and 28m respectively. If the area of each door was 6m², find how many meters of tarpaulin were needed to cover the structure,the width of tarpaulin being 8m.

 

Need the answer quickly!

Answer 1

Dear Sam,

 

Question:  How many meters of tarpaulin were needed to cover the structure, with a tarpaulin of 8m width (assuming no waste...In real life the way the tarpaulin would wrap would create a lot of waste)?

 

     This object is taller than about a three story building.  If you wrap the tarpaulin around the cone, you don't want to cover up the doors, so that a person will be able to go in through them.  This cone is like a person's large living room.   You want to find the lateral area, but not the base.  Why would you want a cover on the base?  You wouldn't. 

 

Lateral area=πrs, where "s" is the slant height of the cone. s=22m, d=28m, so  2r=d,  r=d/2=14 M. A=π(14)(22)=967.6105373 m²

After you find the lateral surface area, (excluding the base), then subtract the total area of 4 doors*6m² =24m² from it.      

 

967.6105373- 24= 943.6105373    Then just divide by 8.                   

 

943.6105373/8  =117.95  Meters of tarp needed    ≅118 Meters   Answer

 

  In the real world, you may want to use 130 M because of wasted material.

 

 

 

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                                                                              Susan C.