Answer: [tex]10\ cm^3[/tex]
Step-by-step explanation:
Given
The surface area of a rectangular prism is [tex]34\ cm^2[/tex]
Width of prism [tex]w=1\ cm[/tex]
Length of prism [tex]l=2\ cm[/tex]
height of prism [tex]h=x\ cm[/tex]
Surface area is given by
[tex]S.A.=2[lw+wh+hl][/tex]
Put values
[tex]34=2[2\times 1+1\times x+2x]\\17=2+3x\\15=3x\\x=5\ cm[/tex]
Now, the volume of Prism is given by
[tex]V=l\times w\times h[/tex]
[tex]\Rightarrow V=2\times1\times 5=10\ cm^3[/tex]
