The sum of radius of the base and height of a cylinder is `37 m.` If the total surface area of the cylinder is `1628 m^(2)`, find the curved surface area and volume of the cylinder

Explanation

Let the radius of the base of the given cylinder be `r` metres and its height be `h` metres
Then, its total surface area
`= (2pi rh + 2pi r^(2)) m^(2)`
`= 2pi r (h +r)m^(2)`
`= (2pi r xx 37) m^(2) " " [ :' (h + r) = 37 ("given")]`
But, total surface area `= 1628 m^(2)`
`:. 2pi r xx 37 = 1628 rArr 2 xx (22)/(7) xx r xx 37 = 1628`
`rArr r= (1628 xx (7)/(44) xx (1)/(37)) m = 7m`
Now, `h + r = 37 rArr h + 7 = 37 rArr h = 30`
`:.` curved surface area of the cylinder
`= (2pirh) m^(2)`
`= (2 xx (22)/(7) xx 7 xx 30) m^(2) = 1320 m^(2)`
Volume of the cylinder
`= (pi r^2)h) m^(3)`
`= ((22)/(7) xx 7 xx 7 xx 30) m^(3) = 4620 m^(3)`