Chapter 6, Problem 84SP

a.

To determine

To explain:The area of an end of the tank can be modelled by $A=2a{\displaystyle \underset{-b}{\overset{b}{\int }}\sqrt{1-{\left(\frac{y}{b}\right)}^2}dy}$

b.

To determine

To prove:The area inside the above ellipse is $\pi ab.$

c.

To determine

To explain:The volume of the fuel at level h $\left(-b\le h\le h\right)$ is modelled by $V=2La{\displaystyle \underset{-b}{\overset{h}{\int }}\sqrt{1-{\left(\frac{y}{b}\right)}^2}dy}$

d.

To determine

To compute: $V(h)$ for $a=5,b=4andL=20$ for $h=-3,-2,-1,\mathrm{...},2,3,4$