Question

the curved surface area of cone is 1159 5/7 cm square and area of its base is 254 4/7 cm square find its volume

Answer 1

hello users ....

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we have given that:
curved surface area of cone = 1159 5/7 = 8118 / 7 cm²

and 
area of its base = 254 4/7 = 1782 / 7 cm²

we have to find :-
volume of cone = ?

solution:-
we know that:
curved surface area of cone = πrl
and 
area of base = πr²

and 
volume of cone = 1/3×πr²h
and 
h = √ (l² - r²)

where,
r is radius , l is slant height , h is height of cone .

According to given:

=> area of base = 1782 / 7 cm²

=> πr² = 1782 / 7

=> 22/7 × r² = 1782 / 7  

=> 22 r² = 1782 

=> r² = 81 

=> r = 9 cm 

And,
=> C.S.area = 8118 / 7

=> πrl = 8118 / 7 cm²

=> 22/7× 9 × l = 8118 / 7 

=> 198 l = 8118

=> l = 41 cm

now,
Height of cone;
=> h = √(l² - r²)

=> h = √ (41² - 9² ) 

= √ (1681 - 81 )

= √ 1600 = 40 cm

now, 
volume of cone = 1/3×π × r² × h 

=> 1/3 × 22/7 × 9² × 40

=> 22×81×40 / 21

=> 3394.28 cm³ Answer 

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✪✪ hope it helps ✪✪

Answer 2

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