Question

Find the ratio between the total surface area of a cylinder to its curved surface area, given that height and radius of the tank are 7.5 m and 3.5 m.

Answer 1

Height of cylinder (h) = 7.5 m

Radius of cylinder (r) = 3.5 m

We know, 

Total Surface Area of cylinder (T.S.A) = 2πr(r+h) 

And, 

Curved surface area of a cylinder(C.S.A) = 2πrh 

Now, 

Ratio between the total surface area of a cylinder to its curved surface area is 

T.S.A/C.S.A = 2πr(r+h)/2πrh 

= (r + h)/h 

= \(\frac{(3.5 + 7.5)}{7.5}\)

= \(\frac{11}{7.5}\)

 = \(\frac{22}{15}\) 

or 22:15

Therefore the required ratio is 22:15.