The curved surface area of a solid cylinder is two-third of the total surface area.If the total surface area is 231 sq.cm. Then what is the volume of the cylinder.

Solution(By Examveda Team)

The total surface area of cylinder
A = 2(pi*r²) + (2*pi*r)*h = 231
Curved surface 2*pi*r*h given as 2/3 of the total
Therefore
2(pi*r r²) would be 1/3 the total; which is 231/3 = 77
Flat ends area
2*(22/7)*r²= 77
(44/7)*r²= 77
r²= 77 * (7/44)
r²- 539/44
r²= 12.25
r = sqrt(12.25)
r = 3.5 cm is the radius
Find h from the curved area; given as 2/3(231) = 154
Substitute 3.5 for r
2*pi*3.5*h = 154
(44/7)*3.5* h= 154
(154/7)*h = 154
h = 154 * (7/154)
h = 7 cm is the height
We know the volume of cylinder = pi* r²*h
V = (22/7)* 3.5² * 7
V = 22 * 12.25
V = 269.5 cm².