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) [latex] \pi [/latex][latex] x^{3} [/latex]+19[latex] \pi [/latex][latex] x^{2} [/latex]+112[latex] \pi [/latex]x+192 B) 2[latex] \pi [/latex][latex] x^{3} [/latex]+35[latex] \pi [/latex][latex] x^{2} [/latex]+80[latex] \pi [/latex]x+48[latex] \pi [/latex] C) 2[latex] \pi [/latex][latex] x^{3} [/latex]+35[latex] \pi [/latex][latex] x^{2} [/latex]+176[latex] \pi [/latex]x+192[latex] \pi [/latex] B) 4[latex] \pi [/latex][latex] x^{3} [/latex]+44[latex] \pi [/latex][latex] x^{2} [/latex]+105[latex] \pi [/latex]x+72[latex] \pi [/latex]

(1) Answers

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

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