Answer
a) $2\sqrt 3$
b)$8$
Work Step by Step
a )
STEP 1) $A(x)$ = $\frac{1}{2}(side)(side)(sin\frac{\pi}{3})$
=$\frac{1}{2}(2\sqrt {sinx}(2\sqrt {sinx})(sin\frac{\pi}{3})$
=$\sqrt 3 \sin x$
STEP 2) $a$=$0$ , $b$=$\pi$
STEP 3 ) $V$=$\int^b_aA(x) dx$
=$\sqrt 3\int^\pi_0\sin x dx$
=$[-\sqrt 3\ cosx]^\pi_0$
=$\sqrt 3(1+1)$
=$2\sqrt 3$
b)
STEP 1 ) $A(x)$ = $(side)^2$
= $(2\sqrt {\ sinx})((2\sqrt {\ sinx})$
=$4 \sin x$
STEP 2) $a$=$0$, $b$=$\pi$
STEP 3)
$V$=$\int^b_aA(x)dx$
= $\int^\pi_04 \sin x \ dx$
=$[-4 \ cos x ]^\pi_0$
= $8$
