 # NCERT Solutions Class 9 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.3 in Chapter 13 - Surface Areas and Volumes

A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm.

Find the area of the sheet required to make 10 such caps. (Assume π=22/7)

The radius of a conical cap, r = 7 cm

Height of conical cap, h = 24 cm

\begin{array}{l} \text { Slant height, } 1^{2}=\left(\Gamma^{2}+h^{2}\right) \\ =\left(7^{2}+24^{2}\right) \end{array}

= ( 49 + 576)

= (625)

Or l = 25 cm

CSA of 1 conical cap = π r l

= 22/7 x 7 x 24

= 550

\begin{aligned} &\text { CSA of } 10 \text { caps }=(10 \times 550) \mathrm{cm}^{2}=5500 \mathrm{cm}^{2}\\ &\text { Therefore, the area of the sheet required to make } 10 \text { such caps is } 5500 \mathrm{cm}^{2} \text { . } \end{aligned}

Video transcript
"hello students welcome to lido q a video session i am seth your math tutor and question for today is a joker's cap is the form of right circular cone of base radius 7 centimeter and height 24 centimeter find the area of the sheet required to make n such gaps assume pi is equal to 22 by 7 now the radius of the conical cap is given that is r is equal to 7 centimeter and height is 24 centimeter apart from this it is given that the area of the sheet required for making 10 such gaps let us find the area of the sheet that is required for one cap to find that we will require the slant height of the cone so slant height here should be l that is equal to under root of h square plus r square so it is under root of 24 square plus 7 square and that is 49 plus 576 root of these two and hence it is if you solve it your slant height is 600 625 root of 625 that is 25 25 centimeter is the slant height that is l now curved surface area of the one conical gap we need to find first curl surface area that is csa of one conical cap we know the formula that is pi r l curl surface area of the cone so it is 22 by 7 into radius is 7 and length slant height that is 24 slant height we have got is 25 so l should be 25 over here and this will give you 550 centimeter square now you know that the car surface area of the one conical cap is 550 centimeter square so 10 such gaps will be just have to multiply 10 with the curl surface area of the one conical cap so curl surface area of one conical cap and therefore current surface area of 10 cap equals to 550 multiplied by 10 and that is 5 5 0 0 5 500 centimeter square is your answer therefore area of sheet required to make 10 such gaps is 5500 centimeter square that is our final answer if you have any queries you can drop it in a comment section and subscribe to lido for more such q a thank you for watching"
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