how many full glasses can be poured

Question

Lemonade is to be poured from a 2 litre bottle into glasses each glass is in the shape of a cylinder of radius 3 centimetre and height 8 centimetre how many full glasses can be poured from this

Answer 1

1)   V = n*v  or    n = V/v   (need to solve for solution)

 

Let V = 2 L bottle

      v = volume of each glass (L)

      n = number of full glasses

 

also, v = a*h*conv

        a = area of glass with radius, r  or ( a = π*r² (cm²)

        r = 3 cm (given glass radius)

        h = 8 cm (given glass height)

        conv = conversion factor = 1 mL/cm³ x 1 L/1000 mL = 0.001 L/cm³

 

Solving for volume of each full glass,

 

v = a*h*conv =  π*r²*h*conv = π*(3 cm)²*(8 cm)*(0.001 L/cm³)

   = π*(9 cm²)*(8 cm)*(0.001 L/cm³) = π*(0.072 L)      

 

Therefore,

 

n = V/v =2 L/(π*(0.072 L)  = 8.84 glasses                              Note: v is equal to L/full glass

 

so rounding up to n = 9 glasses can be filled