I5.1 The volume of a hemisphere with diameter $a \mathrm{~cm}$ is $18 \pi \mathrm{cm}^{3}$, find $a$.
I5.2 If $\sin 10 a^{\circ}=\cos \left(360^{\circ}-b^{\circ}\right)$ and $0<b<90$, find $b$.
I5.3 The triangle is formed by the $x$-axis and $y$-axis and the line $b x+2 b y=120$. If the bounded area of the triangle is $c$, find $c$.

I5.4 If the difference of the two roots of the equation $x^{2}-(c+2) x+(c+1)=0$ is $d$, find $d$.
$\begin{array}{l}\frac{1}{2} \cdot 4 \pi\left(\frac{a}{2}\right)^{2}=18 \pi \\ a=6 \\ \sin 60^{\circ}=\cos \left(360^{\circ}-b^{\circ}\right) \\ 360^{\circ}-b^{\circ}=330^{\circ} \\ b=30 \\ 30 x+60 y=120 \\ \Rightarrow x+2 y=4 \\ x \text {-intercept }=4, y \text {-intercept }=2 \\ c=\frac{1}{2} \cdot 4 \cdot 2=4 \\ x^{2}-6 x+5=0 \\ \Rightarrow(x-1)(x-5)=0 \\ x=1 \text { or } 5 \\ \Rightarrow d=5-1=4\end{array}$