Respuesta :
Answer:
Volume of right square prism = [tex]24\ units^3[/tex]
Step-by-step explanation:
Surface area of right square prism = [tex]50\ units^2[/tex]
Area of square base = [tex]9\ units^2[/tex]
Area of square base is given by = [tex]a^2[/tex]
where [tex]a[/tex] represents the square base edge.
So, [tex]a^2=9[/tex]
Taking square root both sides.
[tex]\sqrt a^2=\sqrt 9[/tex]
[tex]a=3[/tex] [ignoring the -3 as we are finding lengths which is always positive]
Surface area of right square prism is given by =[tex]2a^2+4ah[/tex]
where [tex]a[/tex] represents the square base edge and [tex]h[/tex] represents height of the prism.
So we have,
[tex]2a^2+4ah=50[/tex]
Plugging in values [tex]a=3\ units[/tex] and surface area=[tex]50\ units^2[/tex]
[tex]2(3)^2+4(3)h=50[/tex]
[tex]2(9)+12h=50[/tex]
[tex]18+12h=50[/tex]
Subtracting both sides by 18.
[tex]18+12h-18=50-18[/tex]
[tex]12h=32[/tex]
dividing both sides by 12.
[tex]\frac{12h}{12}=\frac{32}{12}\\\\h=\frac{32}{12}\ units[/tex]
Volume of prism = [tex]a^2h[/tex]
where [tex]a[/tex] represents the square base edge and [tex]h[/tex] represents height of the prism.
Plugging in values [tex]a=3\ units[/tex] and [tex]h=\frac{32}{12}\ units[/tex]
[tex]V=(3)^2\times(\frac{32}{12})\\V=9\times\frac{32}{12}\\\\V=24\ units^3[/tex]
