Question

The volume of a rectangular prism with a square base is fixed at 120 cubic feet. The volume of a rectangular prism with a square base is fixed at 120 cubic feet. Write the surface area of the prism as a function A(x) of the length of the side of the square (x)

Answer 1

A(x)=480/x +2x^2

Explanation:

Answer 2

A(x)=
`2*x^(2) +(480)/(x)`

Explanation:

Length of the side of the square =
`x`

Therefore, Area of the square base =
`x^(2)`

Volume of a prism = Area of the base * Height of the prism

By making the Height of the prism the subject of the equation,

Height of the prism = [Volume of a prism / Area of the base]

Height of the prism =
`(120)/(x^(2) )` feet.

A prism with square base has 6 sides.

Area of the base and the top =
`2*x^(2)`

Area of the sides =
`4*x*(120)/(x^(2) )`

=
`(480)/(x)`

Surface area of the prism A(x)= Area of the base and the top + Area of the sides

=
`2*x^(2)` +
`(480)/(x)`

A(x)=
`2*x^(2) +(480)/(x)`