The total surface area of a solid right circular cylinder is 231 cm^{2}. Its curved surface is ⅔^{rd} of the total surface. Determine the radius of its base and height.

the total surface area of cylinder =231cm^{2}

=> 2πr(r+h)=231 cm^{2}

=> 2πr^{2}+2πrh=231 cm^{2}--------(a)

its curved surface area is=2/3(231)cm^{2} (given)

=> 2πrh=154 cm^{2} --------(b)

putting value of 2πrh from equ. (b) in equ. (a) we get

=> 2πr^{2}+154=231

=>2πr^{2}=231-154

=>2πr^{2}=77

=>r^{2}=77/(2π)

=> r^{2}=12.25 (since π=22/7)

=> r=(12.25)^{1/2} cm = 3.5 cm

to find the value of h

now by putting the value of r=3.5cm in equ. (b) we get

=> 2πrh=154

=> 2(22/7)*3.5* h=154

=> 22h=154

=> h=154/22 cm = 7cm