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

Last updated date: 20th Jun 2024
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Hint: In this particular problem we have to find the curved surface area of one cone using formula $\pi rl$, where r is the base radius and l is the slant height. And then divide this area with the total area given to find the required answer.

Now as we know that the formula for slant height of the cone is $l = \sqrt {{r^2} + {h^2}}$, where r and h are the base radius and height of the cone.
Slant height = $\sqrt {{5^2} + {{12}^2}} = \sqrt {25 + 144} = \sqrt {169} = 13$cm.
Curved surface area of one cap = $\pi rl = \pi \times \left( 5 \right) \times \left( {13} \right) = 65\pi c{m^2}$.
Now as we know that if the area of one cap is $65\pi c{m^2}$ then the number of caps that can be made in the given sheet of paper = $\dfrac{{{\text{Area of sheet of paper}}}}{{{\text{Area of one cap}}}} = \dfrac{{5720}}{{65\pi }} = \dfrac{{5720}}{{65 \times \dfrac{{22}}{7}}} = \dfrac{{5720 \times 7}}{{65 \times 22}} = \dfrac{{40040}}{{1430}} = 28$