The surface area of a rectangular prism is 250 cm 2. If its height is 10 centimeters, and its width is 5 centimeters, what is its volume? 500 cm 3 250 cm 3 200 cm 3 150 cm

Answer:[tex]V=250\ cm^{3}[/tex]Step-by-step explanation:step 1Find the length of the base Lwe know thatThe surface area of a rectangular prism is equal to[tex]SA=2B+PH[/tex]whereB is the area of the baseP is the perimeter of the baseH is the height of the prismsubstitute[tex]SA=2(LW)+2(L+W)H[/tex]we have[tex]W=5\ cm[/tex][tex]H=10\ cm[/tex][tex]SA=250\ cm^{2}[/tex]substitute in the formula and solve for L[tex]250=2(5L)+2(L+5)10[/tex][tex]250=10L+20L+100[/tex][tex]30L=250-100[/tex][tex]L=5\ cm[/tex]step 2Find the volume of the rectangular prismThe volume is equal to[tex]V=(LW)H[/tex]we have[tex]W=5\ cm[/tex][tex]L=5\ cm[/tex][tex]H=10\ cm[/tex]substitute[tex]V=(5*5)*10=250\ cm^{3}[/tex]