Question

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Solve this question!!

"A cone of height 8m has a curved surface area 188.4 square meters.Find it's volume "
(Take π = 3.14)

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Answer 1

hello buddy❗❗❗

solution::

h= 8m

CSA = 188.4

then we know that ,,

CSA of cone=πrl

188.4= 3.14×r×l

r×√r^2+h^2= 188.4÷3.14

r×√r^2+h^2= 60

squaring on both side..

r^2×(r^2+(8)^2)= (60)^2

r^4+ 64r^2-3600= 0

on solving by factorisation method, we get,,,
(r^2-36)(r^2+100)

then the solution are

r^2=36, -100 , since square root of negative no is imaginary no hence,,,
r^2= +-6

radius is positive,,, r= 6m

then we have,,,

Volume of cone= 1/3πr^2×h

= 1/3×3.14×(6)^2×8

=1/3× 3.14×36×8

=3.14×12×8

= 301.44m^3

sorry for the wrong interpret and thanks for a chance...

❕❕be brainlyyy

Answer 2

Here is your solution

Given:-

Height of cone = 8 m

Let radius be r

slant height of cone be l

curved surface are of cone = 188.4 m^2

=>πrl = 188.4

=> 3.14×r√(r^2 + 8^2 ) = 188.4

=> r√(r^2 + 64 ) = 188.4/3.14

=> r√(r^2 + 64 ) = 60

Squaring both sides

=> r^2 ×(r^2 + 8r ) = (60)^2

=> r^4 + 64r^2 = 3600

=> r^4 + 64r^2 - 3600 = 0

=> (r^2 - 36)(r^2 + 100) = 0

=> r^2 = 36, -100

Hence radius is 6 m.

Now

volume of the cone

=(1/3)×πr^2 h                      

 = (1/3)π×6^2h

= (1/3×3.14×36×8)

= 1/3×3.14×36×8

=(3.14×36×8)/3

= 301.44 m^3

Hope it helps you