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