Question

10 square pieces of foam board each with an area of 169 square inches be cut in used to construct a cube with a volume of 1728 cubic inches explained 1.yes the side lengths of boards is greater than the side of the cube 2.yes the area of Ford is greater than the volume of the cube 3.no the side length of board is less than the side of the cube 4.know the area of board is less than the volume of the cube

Answer 1

10 square pieces each have area of 169 square inch,

expression for the area of square is

$\text{Area of square =side}^2$

Since, area is given, plot the value and solve for the measurement of the side of square,

$\begin{gathered} \text{side}^2=169 \\ \text{side}=13\text{inch} \end{gathered}$

The cube has the same length, breadth as well as hieght so the volume of cube is :

$\text{Volume of cube =side}^3$

the volume of the cube is given, substitute the volume=1728, and solve for dimension of the cube,

$\begin{gathered} \text{Volume of cube =side}^3 \\ \text{side}^3=1728 \\ \text{side}=12\text{ inch} \end{gathered}$

so, the length of board is 13, which have to be cut to to become 12 inch for making cube,

Answer :

1. yes, the side length of the board is greter than the side of cube.