Question

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.

Answer 1

r + h = 37 m
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

Answer 2

given,
     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