Final answer:
To find the number of rocks that can be placed in the beaker without sinking, we need to calculate the volume of the beaker and the volume of each rock. We can then divide the volume of the beaker by the volume of each rock to get the number of rocks.
Step-by-step explanation:
The first step is to calculate the volume of the beaker. Since one-quarter of its height is submerged in water, the submerged height is 12.0 cm / 4 = 3.0 cm. The volume of the beaker is equal to the volume of water displaced, which is given by the formula V = πr 2h, where r is the radius and h is the height. The radius of the beaker is half of its diameter, so the radius is 5.00 cm / 2 = 2.50 cm. Plugging these values into the formula, the volume of the beaker is V = π(2.50 cm)²3.0 cm) = 58.91 cm³.
Next, we need to calculate the volume of each rock. The density of each rock is given as 15.0 g. To find the volume, we can use the formula V = m / ρ, where m is the mass and ρ is the density. Plugging in the values, we get V = 15.0 g / (15.0 g/cm³) = 1.0 cm³.
Finally, to determine the number of rocks that can be placed in the beaker without sinking, we divide the volume of the beaker by the volume of each rock. N = V(beaker) / V(rock) = 58.91 cm³ / 1.0 cm³ = 58.91.