To solve this problem we will first proceed to find the volume of the hemisphere, from there we will obtain the mass of the density through the relation of density. Finally the mass of the stone will be given between the difference in the mass given in the statement and the one found, that is
The volume of a Sphere is
[tex]V = \frac{4}{3} \pi r^3[/tex]
Then the volume of a hemisphere is
[tex]V =\frac{1}{2} \frac{4}{3} \pi r^3[/tex]
With the values we have that the Volume is
[tex]V =\frac{1}{2} \frac{4}{3} \pi (8.4/2)^3[/tex]
[tex]V = 155.17cm^3[/tex]
Density of water is
[tex]\rho = 1g/cm^3[/tex]
And we know that
[tex]\text{Mass of water displaced} = \text{Density of water}\times \text{Volume of hemisphere}[/tex]
[tex]m = 1g/cm^3 * 155.17cm^3[/tex]
[tex]m = 155.17g[/tex]
So the net mass is
[tex]\Delta m = m_s-m_w[/tex]
[tex]\Delta m = 155.17-23[/tex]
[tex]\Delta m = 132.17g[/tex]
Therefore the mass of heaviest rock is 132.17g or 0.132kg
The mass of the heaviest rock that, in perfectly still water, won't sink the plastic boat is 155 g.
We know that the density of water = 1 g/cm^3
Volume of the hemisphere = 2/3 πr^2
When diameter = 8.4 cm, radius = 4.2 cm
So, V = 2/3 × 3.14 × (4.2)^3
V = 155 cm^3
Volume of hemisphere = volume of water displaced = 155 cm^3
Mass of water displaced = 155 g
Since the solid displaces its own mass of water, the mass of the heaviest rock that, in perfectly still water, won't sink the plastic boat is 155 g.
Learn more about principle of flotation: https://brainly.com/question/16000614
