Question

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 -

Answer 1

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.

Answer 2

thanks

Answer 3

No probs. :)