Precella590
14

~~~20 POINTS~~~ Carol is designing an oatmeal container. Her first design is a rectangular prism with a height of 12 inches, a width of 8 inches, and a depth of 3 inches. a. What is the total surface area of the container to the nearest square inch? Use 3.14 for $\pi$. b. Carol wants to redesign the package as a cylinder with the same total surface area as the prism in part α. If the radius of the cylinder is 2 inches, what is the height of the cylinder? Round your answer to the nearest inch. Use 3.14 for $\pi$.

I'm so sorry for the late answer! (a) Rectangular container There are 3 pairs of congruent sides. Each side's area can be solved by multiplying either 12, 8, or 3. Then because for each side, there is another side that is exactly the same, we can multiply by 2. (2*12*8) + (2*12*3) + (2*8*3) = 312 (b) Surface Area of a cylinder is $2 \pi r^{2} +2 \pi rh$ We know that r is 2 and that the whole expression is equal to 312. Plug 2 back into the equation and set it equal to 312. $2 \pi *4+2 \pi *2h = 312 \\ 4 \pi *h = 312-8 \pi \\ h = \frac{312-8 \pi }{4 \pi } = 23$ The height of the cylinder has to be around 23 inches.