Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 296: 1

a) $A$ = $\frac{4}{25}(20-y)^{2}$ b) $V$ = $\frac{1280}{3}$

a) s = side length y = height $\frac{8}{20}$ =$\frac{s}{20-y}$ $s$ = $\frac{2}{5}(20-y)$ $A$ = $(s^{2}$ $A$ = $\frac{4}{25}(20-y)^{2}$ b) $V$ = $\int_0^{20}\frac{4}{25}(20-y)^{2}dy$ $V$ = $-\frac{4}{75}(20-y)^{3}|_0^{20}$ $V$ = $\frac{1280}{3}$