The total surface area of a solid right circular cylinder is 231 cm². Its curved surface is ⅔^rd of the total surface. Determine the radius of its base and height.

 the total surface area of cylinder =231cm²

=> 2πr(r+h)=231 cm²

=> 2πr²+2πrh=231 cm²--------(a)

its curved surface area is=2/3(231)cm² (given)

=> 2πrh=154 cm² --------(b)

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

=> 2πr²+154=231

=>2πr²=231-154

=>2πr²=77

=>r²=77/(2π)

=> r²=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