## anonymous 5 years ago The height of a right circular cylinder is 6m. Three times the sum of the areas of its 2 circular faces is twice the area of its curved surface. The radius of its box is -

1. anonymous

Let the area of each circular face be $A_c$and the area of the cap (the curved surface),$A_s$Then 3 times the sum of the areas of the circular faces is$3(A_c+A_c)=6A_c$and this is equal to twice the area of the curved surface, so$6A_c=2A_s$Now, $A_c=\pi{r^2}$and$A_s=2\pi{r}h=2\pi{r}6=12\pi{r}$Subbing into the equation linking the two above, $6(\pi{r^2})=2(12\pi{r})\rightarrow r^2-4r=0$which means either r=0 or r=4. If r=0, you have no cylinder going on, so r = 4 metres.

2. anonymous

thanks

3. anonymous

No probs. :)