# The sum of the radius of the baseand height of a solid cylinder is 37m. If the total surface area of the solid cylinder is 3256 sq.m. , find the volume of the cylinder.

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by Anmol20RK

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by Anmol20RK

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Total surface area = 2πr(r+h)

2πr(r+h) = 3256

2πr×37 = 3256

r = 3256/74π

r = 14

h = 23

π = 3.1415926

Volume of the cylinder = πr²h

= π×196×23

= 14162.3

the surface area of solid cylinder = 2πr (r+h) = 3256 sq.m

let,

radius =r , height = h

r+ h = 37

2πr(37) = 3256

2 ×22/7 ×r(37) = 3256

44/7 × 37r = 3256

44×5.2 r = 3256

232.5 r = 3256

r =3256/232.5

r = 14 m

h= 37-14 =23 m

volume of cylinder = πr²h

= 22/7 ×14² ×23

= 22 ×2×14×23

= 14168 m³