Respuesta :
Answer:
W is concave up.
Step-by-step explanation:
We are filling a spherical tank starting at the top half (meaning it is fulled half initially) at a constant rate. So, the tank level will increase in proportion to the tank's diameter at a given height.
Since the area of the circle is π·r² , then W(t) will be an increasing curve of second degree.
So, the curve for W(t) is concave up.
Also, the tank level increases over time at a more rapid rate.
Hence, the graph of W is concave up.
Answer with explanation:
Let V be the volume of the tank.
Water is being poured into the spherical tank at a constant rate.
Let r, be the radius of spherical tank.
[tex]\frac{dr}{dt}=\text{Constant}=r[/tex]
As, radius is constant. --------------------------------(1)
Volume of tank will increase with time.
So,⇒ Height of sphere=Radius of sphere
Volume of Spherical tank
[tex]V=\frac{4\pi r^3}{3}\\\\\frac{dv}{dt}=4\pi r^2\frac{dr}{dt}\\\\=4\pi r^2\times r [/tex]
-----------------[using (1)]
So,
[tex]W(t)=4\pi r^3[/tex]
