Question

use & model a toy manufacturer produces a set of blocks, with edge (b), that can be used by children to build play - structures. the production team is analyzing the amount of paint they need for a block.
a. the production team decides to use one coat of paint for each block. write an expression representing the minimum amount of paint needed for one block with edge (b).
b. the production team decides one coat of paint is not enough, so they need to use two coats of paint for each block. write an expression representing the minimum amount of paint needed for one block with edge (b).

Explanation:

Step1: Recall surface - area formula for cube

The surface - area formula of a cube with edge length $b$ is $S = 6b^{2}$. One coat of paint covers the surface - area of the cube.

Step2: Answer part A

For one coat of paint, the minimum amount of paint needed is equal to the surface - area of the cube. So the expression is $6b^{2}$.

Step3: Answer part B

If two coats of paint are needed, we multiply the surface - area by 2. The expression is $2\times6b^{2}=12b^{2}$.

Step4: Answer part C

If one can of paint covers 60 square inches and two coats of paint are used (so the surface - area to be covered is $12b^{2}$), the inequality representing the maximum length of edge $b$ is $12b^{2}\leq60$.

Answer:

A. $6b^{2}$
B. $12b^{2}$
C. $12b^{2}\leq60$