Height = 7cm
Surface area = 462 cm2
The surface area of a cylinder is equal to the area of each circle ( pi x radius^2) plus the area of the side (2 pi x radius x height)
Surface area of a cylinder = pi r2 + pi r2 + 2pi r h
Since it is closed at one end, we only add one circle area:
S = pi r2 + 2pi r h
Replacing with the values given:
462 = pi r^2 + 2pi (r) 7
462 = pi r^2+ 43.98 r
462 -44r = pi r^2
(462-44r)/pi = r^2
147-14r = r^2
0= r^2 +14r -147
(r+21 ) (r-7)=0
r=-21 or r=7
Since it can be negative:
radius = 7