I hope this helps you
5000.pi=4/3.pi.r^3
r^3=3750
r=15,53
Surface Area=4pir^2
Surface Area =4.pi. (15,53)^2
Surface Area =964,72.pi
First picture:
You got the first two right (good job!), so I'll just tackle the third one. If you have to compute , it means that you have to substitute in place of . Differently from the first two points, this will generate a new function, rather than a specific value:
Second picture:
Given the point highlighted in the picture, you can deduce that the base is units long (since it spans from to ) and the height is units long (because it spans from to ). So, the area of the rectangle is the multiplication between base and height:
But we know that , so we have
The domain of this function is given by the domain of the square root: we want its argument to be non, negative, so we have
But since the problem is symmetric, the answer is
You can only see the answer because, if you choose or , the rectangle degenerates to a segment, and your exercise doesn't like this scenario, apparently
reflexive postulate of equality
There are no equations? Well there’s no picture