Sum

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 cm^{2}, how many caps can be made with radius 5 cm and height 12 cm.

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#### 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 cm^{2}

Number of caps = `"Total area of the paper"/"Area of paper for one cap"`

= `(5720 xx 7)/(22 xx 65)`

= 28 caps

Concept: Surface Area of Cylinder

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