Question

125 marbles of diameter 1.2 cm are dropped into a beaker containing some water and are fully submerged if the diameter of the beaker is 6cm calculate the rise in water in the beaker

Answer 1

Answer:

The water will rise by

h = 3.9994872339 cm

or

h = 4cm approx

Step-by-step explanation:

r = d/2

radius of marble is

r = 1.2 ÷2

= 0.6 cm

Volume of one marble is

V = 4/3 × π × r^3

= 4/3 × 3.142 × 0.6 ^3 ≈ 0.90478 cubic cm

Volume of all 125 marbles = 125 × 0.90478 cubic cm

= 113.0975 cubic cm

diameter of beaker = 6 cm

r = d/2 =3 cm

area of base of beaker = π × r^2

= 3.142 × 9

= 28.278 sq cm

so the water will rise by

h = Volume of marbles ÷ area of the base of beaker

= 113.0975 ÷ 28.278

= 3.9994872339

or

h = 4cm approx