The total surface area of a cylinder of radius `7 cm` is `880 cm^(2)`.
Find the height and the volume of the cylinder

Explanation

Given, `r = 7 cm.` Let the height of the cylinder be `h` cm.
Then, total surface area `= (2pi r^(2) + 2pi rh)` sq units
`= 2pi r (r + h)` sq units
`= 2 xx (22)/(7) xx 7 xx (7 + h) cm^(2)`
`= 44 (7 + h) cm^(2)`
`:. 44 (7 + h) = 880 rArr (7 + h) = 20 rArr h = (20 - 7) = 13`
Hence, the height of the cylinder is `13 cm`
Volume of the cylinder `= (pi r^(2)h)` cubic units
`= ((22)/(7) xx 7 xx 7 xx 13) cm^(3) = 2002 cm^(3)`
Hence, the volume of the cylinder is `2002 cm^(3)`