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Question
A girl wishes to prepare birthday caps in the form of right circular cones for her birthday party, using a sheet of paper whose area is 5720 cm2, how many caps can be made with radius 5 cm and height 12 cm.
Solution
Radius of a cap (r) = 5 cm
Height of a cap (h) = 12 cm
l = `sqrt("h"^2 + "r"^2)`
= `sqrt(12^2 + 5^2)`
= `sqrt(144 + 25)`
= `sqrt(169)`
= 13
C.S.A. of a cap = πrl sq. units
= `22/7 xx 5 xx 13 "cm"^2`
= `(22 xx 65)/7 "cm"^2`
Total Area of a sheet of paper = 5720 cm2
Number of caps = `"Total area of the paper"/"Area of paper for one cap"`
= `(5720 xx 7)/(22 xx 65)`
= 28 caps
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