Question

the total surface area of a solid right circular cylinder is 231 cm². its curved surface is 2/3rd of the total surface. find the radius of the base and height.

Answer 1

so total surface area of a cylinder = 2πrh + 2πr²
curved surface area = 2πrh

so 2/3 x (2πrh + 2πr²) = 2πrh
2/3 x (h + r ) = h
2h + 2r = 3h 
h = 2r

so 2πrh + 2πr² = 231

2πr(h + r) = 231
2πr x 3r = 231
r = √231/6π
 r = 3.5 cm 
and h = 2r 
   h = 7 cm

So r = 3.5 cm and h = 7 cm

Answer 2

Total surface area of a solid circular cylinder = 231 cm²
Its curved surface area = 2πrh
Total surface area = 2πrh + 2πr²
 2πrh + 2πr² = 231............. - (1)
Curved surface area is 2/3rd of the total surface area
Therefore,
2πrh = 2/3 * 231
2πrh = 154................ - (2)
Substituting value of 2πrh from equation (2) into equation (1), we get,
154 + 2πr² = 231
2πr² = 231 - 154
2πr² = 77
2 * 22/7 * r² = 77
44/7 r² = 77
r² = 77 / 44/7
r² = 77 * 7 / 44
r² = 539 / 44
r² = 12.25
r = √12.25
r = 3.5 cm
Substituting r's value in equation (2), we get,
2 * 22/7 * 3.5 * h = 154
(44 * 3.5)h / 7= 154
22h = 154
h = 154 / 22
h = 7 cm
Therefore, radius = 3.5 cm and height = 7 cm.