A right circular cylinder has a radius of 8 inches and a height of 4 inches. Decrease the height and radius by \( 10 \% \). Use the formulas \( \mathrm{V}=\pi \mathrm{r}^{2} \mathrm{~h} \) and \( \mathrm{SA}=2 \pi \mathrm{rh}+2 \pi \mathrm{r}^{2} \) to answer parts a through d below. a. Find the volume V and surface area SA of the original cylinder.

Let's calculate the original volume and surface area of the right circular cylinder with a radius \( r = 8 \) inches and height \( h = 4 \) inches. The volume \( V \) of the cylinder is given by the formula \( V = \pi r^{2} h \): \[ V = \pi (8)^{2} (4) = \pi (64)(4) = 256\pi \text{ cubic inches.} \] Now, let’s find the surface area \( SA \): \[ SA = 2 \pi rh + 2 \pi r^{2} = 2 \pi (8)(4) + 2 \pi (8)^{2}. \] Calculating each term: - For the lateral area: \( 2 \pi (8)(4) = 64\pi \) - For the areas of the two bases: \( 2 \pi (8)^{2} = 128\pi \) So, \[ SA = 64\pi + 128\pi = 192\pi \text{ square inches.} \] Thus, the original cylinder has a volume of \( 256\pi \) cubic inches and a surface area of \( 192\pi \) square inches.