Question

Please Solve It. It's Urgent! (Points-50)

Find the length of cloth used in making a conical pandal of height 100m and base radius 240m, if the cloth is 100pie m wide.

Please elaborate and answer. :)

Answer 1

i)the dimensions of the cloth
length= l m
width =w=100pi m
area of the cloth = lw
= l*100 pi m^2----(1)
ii)dimensions of the conical pondal
height =H=100m
radius =r=240m
slant height =Lm
L^2= r^2+H^2
=(240)^2+(100)^2
=57600+10000
=67600
L= 260m

csa of the cone = pi*r*L m^2
=pi*240*260---(2)
(1)=(2)
l*100*pi=pi*240*260
l=(pi×240*260)/(100*pi)
l=24*26
l=624 m
length of the cloth required=l=624m

Answer 2

Pandal is in the shape of a conical surface.  It is not mentioned if the pandal also includes cloth for flooring inside the conical shape.

The radius R of base circle ,  the altitude (height) H and the Slant height S make a right angle triangle.
So  S² = R² + H² = 100² + 240² = 67600  m²
      S = 260 m
   (we can calculate this easily as we know 5, 12, 13 make a right angle triangle.  Here  100, 240 are 20 times these numbers.) 

The surface area of the Conical shape gives the area of the cloth required.
CSA  curved surface area:  π R S = π * 240 * 260 m²

The cloth used is in rectangular shape. So the length required 
    =  area/ width = π * 240 * 260 / (100 π) = 624 m

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If the base circular area of pandal (floor) is also to be included for calculations then  the total surface area of cone is to be used.
TSA = π R (R+H) = π 240 (240+260) = π 120, 000 m²

Then the length of cloth required will be =  π*120,000/ (100 π)
       = 1,200 m.

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In such exercises, sometimes we need to find width or height or length of cloth, without having to cut it into pieces and then stitch them together again into the shape required.

Here in this exercise, nothing is mentioned related to cutting or not cutting the given cloth into pieces and stitching them again.