Question

the curved surface area of a cone is 1159×5/7 cm^2. area of its base is 254×4/7cm^2 .find it's volume?​

Answer 1

Answer:

Step-by-step explanation:

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