Question

15. 3080 cm3 of water is required to fill a cylindrical vessel completely and 2310 cm3 of water is required to fill it upto 5 cm below the top. .Find :

(i) radius of the .vessel. (ii) height of the vessel.

(iii) wetted surface area of the 'vessel when it is half-filled with water.

Answer 1

i) 22/7*r^2*h = 3080
22/7*r^2*(h-5) = 2310
r^2*h = 3080*7/22
= 280
22/7*r^2*h-22/7*r^2*5
22/7*280-22/7*r^2*5 = 2310
22/7(280-r^2*5) = 2310
280-r^2*5 = 2310*7/22
= 735
-r^2*5 = 735-280
= 455
r^2 = 455/5
= 91
therefore r = root 91
ii) r^2*h = 280
h = 280/91
therefore h = 3.07
iii) height = 3.07/2
csa + base area = 2*22/7*root 91*3.07/2+ 22/7*root 91^2
= 295.64 root 91 cm^2
hope it is right