The respective ratio of curved surface area and total surface area of a right circular cylinder is 3 : 5. If the curved surface area of the right circular cylinder is 1848 cm^2 . what is its height? (in cm.)

Explanation:

Radius of cylinder = r cm and height = h cm (let)

According to the question,

Curved surface area = 2 πrh

Total surface area = 2 π rh + 2 πr^2

∴ 2πrh\2πr(h+r) = 3\5

=> h\h+r = 3\5

=> 5h = 3h + 3r

=> 2h = 3r …..(i)

Again, 2 π rh = 1848

=> 2 π × 23 h × h = 1848

[From equation (i)]

=> 2 × 22\7 × 2\3 h^2 = 1848

=> h^2 = 1848×7×3\2×22×2

= 21 × 21

=> h = √21×21 = 21 cm