Answer: (a) 2 : 3
(b) 4 :1
Step-by-step explanation:
[tex]\\[/tex]The Volume of a sphere is given as
[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex] and the volume of a cylinder is given as [tex]\pi[/tex][tex]r^{2}[/tex]h
[tex]\\[/tex]The ration of their volume is the same as Volume of Sphere : Volume of Cylinder , which gives
[tex]\\[/tex][tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex] : [tex]\pi[/tex][tex]r^{2}[/tex]h
[tex]\\[/tex]recall that they have the same radius and the height of the cylinder is 2r , taking this into consideration, we have
[tex]\\[/tex][tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex] : [tex]\pi[/tex][tex]r^{2}[/tex](2r)
[tex]\\[/tex]which gives 4 : 6 = 2 :3
[tex]\\[/tex](b) The area of a sphere is 4[tex]\pi[/tex][tex]r^{2}[/tex] and the surface area of the circular cylinder is [tex]\pi[/tex][tex]r^{2}[/tex]
[tex]\\[/tex]The ratio then gives
[tex]\\[/tex]4[tex]\pi[/tex][tex]r^{2}[/tex] : [tex]\pi[/tex][tex]r^{2}[/tex] ,which gives
[tex]\\[/tex]4 : 1
