The ratio of curved surface area and volume of a cylinder is 1 : 7. The ratio of total surface area and volume is 187 : 770. What is the respective ratio of its base radius and height?
We have :
$$2\pi\ rh\ :\pi\ r^2h\ =1:7$$
we get 2:r = 1:7 (1)
r= 14
From 2nd condition we get :
$$2\pi\ r\left(r+h\right)\ :\pi\ r^2h\ =187:770$$ Â (2)
Substituting r=14 in (2)
we get h =20
Therefore r:h = 7:10
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