Question

Find the number of cylindrical glasses of diameter 6cm and height 80mm that can be filled with juice from a cylindrical vessel of base diameter 30cm, given that the vessel is filled with juice upto a height of 32cm.

Answer 1

Height of vessel, H = 32 cm
Diameter of vessel, D = 30 cm 
i.e. R = 15 cm

Height of glass, h = 80 mm
                             = 8 cm
Diameter of glass, d = 6 cm
i.e. r = 3 cm 

Let the no of glasses that can be filled = x

Therefore,
the Volume of vessel = x times the volume of glass
⇒ $\pi R$² H   = $\pi r$² h * x
⇒$\pi$ * 15* 15 *32 = $\pi$ * 3 * 3* 8 * x
⇒$\pi$ * 15* 15 *32 / $\pi$ * 3 * 3* 8 = x
⇒ x = 5*5*4
⇒ x = 100

Therefore, the no. of glasses that can be filled = x
                                                                          = 100