We are given the ratio
A : C = 4 : 1
where
A=area = pi*r^2
[tex]A=\pi r^2[/tex]
C=circumference = 2pi*r
[tex]C=2\pi r[/tex]
then
[tex]\pi r^2:2\pi r=4:1[/tex]
express as afraction
[tex]\frac{\pi r^2}{2\pi r}=\frac{4}{1}[/tex]
thus
[tex]\frac{r}{2}=4[/tex][tex]r=2*4=8[/tex]
then the radius is r=8cm
B)Circumference
[tex]C=2\pi r=2\pi8=16\pi[/tex][tex]C=16*3.14=50.24[/tex]
the circumference is 50.2 cm
C)Area
[tex]A=\pi r^2[/tex][tex]A=3.14*8^2=200.96[/tex]
then the Area is 201.0 cm^2
D)Volume
[tex]V=\frac{4}{3}\pi r^3[/tex][tex]V=\frac{4}{3}*3.14*8^3[/tex][tex]V=2143.573[/tex]
then the volume is
V=2143.6 cm^3