1) In Fig. 1, from \( P \) secants \( P D A \) and \( P B C \) are drawn so that; \( m(A P C)=30^{\circ} \), chord \( \overline{A B} \) and \( \overline{C D} \) intersect at \( F \) to form \( m(A \hat{F} C)=85^{\circ} \). Find the \( m(\operatorname{arc}(A C)), m(\operatorname{arc}(B D)) \) and \( m(A \hat{B} C) \). Fig. 1 2) Find the diameter, in centimeters, of a sphere with volume \( 36 \pi \mathrm{cm}^{3} \) 3) Find the volume of frustum whose upper and lower bases are circular regions of radii \( 4 \mathrm{~cm} \) and \( 2 \mathrm{~cm} \) respectively, is \( 9 \mathrm{~cm} \) deep. 4) Write the equation of the circle tangent to the \( x \)-axis at \( (6,0) \) whose center is on the line \( x-2 y=0 \). 5) Find the foci of the conic \( 9 x^{2}-4 y^{2}-72 x+8 y+176=0 \) and sketch its graph.