Question

1. A perspex box has a 10 cm square base and contains water to a height of 10 cm. A piece of rock of mass 600g is lowered into the water and the level rises to 12 cm.

(a) What is the volume of water displaced by the rock?
(b) What is the volume of the rock?
(c) Calculate the density of the rock

Answer 1

(a) The volume of water is 100 cm³

(b) The volume of the rock is 20 cm³

(c) The density of the rock is 30 g/cm³

Step-by-step explanation:

The given parameters of the perspex box are;

The area of the base of the box, A = 10 cm²

The initial level of water in the box, h₁ = 10 cm

The mass of the rock placed in the box, m = 600 g

The final level of water in the box, h₂ = 12 cm

(a) The volume of water in the box, 'V', is given as follows;

V = A × h₁

∴ The volume of water in the box, V = 10 cm² × 10 cm = 100 cm³

The volume of water in the box, V = 100 cm³

(b) When the rock is placed in the box the total volume,
`V_T`, is given by the sum of the rock,
`V_r`, and the water, V, is given as follows;

`V_T` =
`V_r` + V

`V_T` = A × h₂

∴
`V_T` = 10 cm² × 12 cm = 120 cm³

The total volume,
`V_T` = 120 cm³

The volume of the rock,
`V_r` =
`V_T` - V

∴
`V_r` = 120 cm³ - 100 cm³ = 20 cm³

The volume of the rock,
`V_r` = 20 cm³

(c) The density of the rock, ρ = (Mass of the rock, m)/(The volume of the rock)

∴ The density of the rock, ρ = 600 g/(20 cm³) = 30 g/cm³