Question

A solid cylinder has total surface area of 462cm^2.its curved surface area is one-third of its total surface area.find the radius and height of cylinder ?

Answer 1

Answer:

So, the radius is 7cm and height is 3.5 cm

Step-by-step explanation:

Total surface area (TSA)  = 462 cm^2

Curved surface area (C.S.A) = 1/3 of T.S.A

= 1/3 * T.S.A = 1/3 * 462

= 462/3 = 154 cm^2

C.S.A = 2* πrh

T.S.A = 2πr (r + h)

Therefore, T.S.A/C.S.A = 2πr (r + h)/ 2πrh

= (r + h)/ h

T.S.A /C.S.A = 462/154 = 3

Therefore, we have (r + h)/h = 3

r + h = 3h

r = 2h

So, C.S.A = 2* πrh

154 = 2*22/7 *r * r/2

154 = 22/7 * r^2

r^2 = 154 * 7/22

r^2 = 7^2

Therefore, r = 7 cm

So, h = r/2 = 7/2 = 3.5 cm

So, the radius is 7cm and height is 3.5 cm