Aresearch biologist requires a sturdy yet floatable plastic sphere to carry out a lake project within a local wildlife refuge. the spheres have a diameter of 51.75mm what is the maximum allowable mass the sphere can be in order to remain afloat ? assume the density of water in the lake is 1.0 g/cm^3 at all times throughout the year

The maximum allowable mass is 580 g.

Step 1. Calculate the volume of the spheres

V = (4/3)πr^3 = (4/3)π × (51.75 mm^3) = 5.8052 × 10^5 mm^3

Step 2. Convert the volume to cubic centimetres

V = 5.8052 × 10^5 mm^3 × (1 cm/10 mm)^3 = 580.52 cm^3

Step 3. Calculate the mass of water displaced

According to Archimedes’ principle, each sphere displaces

580.52 cm^3 water

Mass of water = 580.52 cm^3 water × (1.0 g water/1 cm^3) = 580 g water

If the mass of a sphere is greater than the mass of water displaced, the sphere will sink.

∴ The maximum allowable mass of the sphere is 580 g.

that's just how they are

explanation:

you can't control another persons decisions, all you can do is ask that they respect yours. relationships are hard because you have to put the effort into making sure that another person feels seen, heard, and loved. as time goes on, it gets easier, you learn how to do these things without thinking. loving them becomes as easy as breathing, but every relationship will have fights, and sometimes it'll feel like you're drowning, but as long as you can talk it out and compromise, because that's truly what loving another person is, is compromise, then you'll be okay. movies and tv shows have glamorized and romanticized (pardon the pun) what a relationship would be like. real relationships aren't perfectly timed kisses in the rain, zero fights until one big one ends everything, 6 month anniversaries. real relationships are sleepy confused kisses when one person has to leave for work earlier than the other,   real relationships are having small disagreements, real relationships are messy and confusing, real relationships is knowing that even if you're relationship may not last forever and this may not be the person you're going to spend the rest of your life with, that you love them, and you would do anything to see them happy. so yes, relationships are difficult, but so are many other things, relationships can be amazing but also stressful, and not just romantic i'm also talking about platonic relationships (although the primary example here was romantic) sometimes is best to leave friendships behind, so remember, always do whats going to you be happy in the long run.