Question

Suppose you have a coffee mug with a circular cross section and vertical sides (uniform radius). What is its inside radius if it holds 400.0 g of coffee when filled to a depth of 6.00 cm? Assume coffee has the same density of water. Answer in cm.

Answer 1

Coffee mug is cylindrical shape. Therefore, 
Volume of mug = volume of cylinder = πr²h 

r = inner radius of mug. h = height of coffee = 6 cm. 
Density of coffee = Density of water = 1 g/ml 

Therefore, volume of coffee = mass/density = 400/1 = 400 ml = 400 cm³
Volume of coffee = πr²h
400= πr²(6) 
r² = 21.23
r = inner radius of mug = 4.607 cm