Question

Frozen specimens are stored in a cubic metal box that is x inches on each side. The box is surrounded by a 2-inch-thick layer of Styrofoam insulation.

a) Find a polynomial function V(x) that gives the total volume in cubic inches for the box and insulation.​

Answer 1

Answer:

Since 2 inches of foam is added all around the box, the sides are now x + 4 inches each. The volume of a cube is the cube of the side.

$V(x) = (x+4)^3$

Answer 2

Given: Frozen specimens are stored in a cubic metal box that is x inches on each side. The box is surrounded by a 2-inch-thick layer of Styrofoam insulation.

To find: Find a polynomial function V(x) that gives the total volume in cubic inches for the box and insulation.​

Solution:

Know that the side of the cubic metal box is $x$ inches.

Observe the given figure that, the metal box is insulated with a 2 inch thick styrofoam.

Therefore, the side of the new cube will be $(x+2+2)=(x+4)inches$.

Write the polynomial function for the total volume in cubic inches for the box and insulation.​

Assume that, $V(x)$ is the volume of the in cubic inches for the box and insulation.​

$\[\begin{array}{l}V\left( x \right) = \left( {x + 4} \right) \times \left( {x + 4} \right)\\ \Rightarrow V\left( x \right) = {\left( {x + 4} \right)^2}\end{array}\]$

Therefore, the  polynomial function V(x) that gives the total volume in cubic inches for the box and insulation is $\[V\left( x \right) = {\left( {x + 4} \right)^2}\]$.