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 g of coffee when filled to a depth of 8.00 cm? assume coffee has the same density as water.

Answer 1

Coffee mug is cylindrical in shape. So, volume of cylinder = V=π r² h Mass of coffee = 400 g which is filled to a depth of 8.00 cm. so, h=8.00 cm density of water = 1 g/cm³ Density = mass/volume 1 g/cm³ = 400g / volume volume = (400g) / (1 g/cm³) volume = 400 cm³ As, volume of cylinder - V=π r² h 400 cm³ = π r^2 x 8.00 cm π r² = (400 cm³) / (8.00 cm) π r² = 50 cm² r² = (50)/ π r² = 15.924 cm² Taking square root on both sides - r =3.99 cm r =4.00 cm Answer: Thhe inside radius of coffee mug is 4.00 cm