jessbelle
34

# The volume of a cylinder is given by the formula V=(pi)(r^2)(h), where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius (x + 8) and height (2x + 3). Which expression represents the volume of the can? A) $\pi$$x^{3}$+19$\pi$$x^{2}$+112$\pi$x+192 B) 2$\pi$$x^{3}$+35$\pi$$x^{2}$+80$\pi$x+48$\pi$ C) 2$\pi$$x^{3}$+35$\pi$$x^{2}$+176$\pi$x+192$\pi$ B) 4$\pi$$x^{3}$+44$\pi$$x^{2}$+105$\pi$x+72$\pi$

Volume of cylinder = $\pi r^{2}h$ Substituting $r=x+8$ and height = $2x+3$ Volume = $\pi (x+8)^{2} (2x+3)$, expanding the $(x+8)^{2}$ Volume = $\pi ( x^{2} +16x+64)(2x+3)$, expanding the last two brackets Volume = $\pi ( 2x^{3}+3 x^{2} +32 x^{2} +48x+128x+192)$, then simplify Volume = $\pi ( 2x^{3} +35 x^{2} +176x+192)$, then mulitply out pi Volume = $2 \pi x^{3}+35 \pi x^{2} +176 \pi x+192 \pi$