Question

Toy manufacturer's block production:

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 want 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.
c. The production team purchases cans of paint that will cover 60in^2. Write an inequality representing the maximum length of edge b, in inches, when the block is covered with the minimum amount of paint needed for two coats of paint.

Answer 1

To find the minimum amount of paint needed for one block with edge b, the surface area of the block needs to be determined. The expressions for one coat and two coats of paint are 6b^2 and 12b^2, respectively. The maximum length of edge b, in inches, can be found using the inequality 12b^2 ≤ 60.

Step-by-step explanation:

a. To find the minimum amount of paint needed for one block with edge b, we need to determine the surface area of the block. A cube has six equal faces, so the surface area of one face is b^2. Since there are six faces, the total surface area is 6b^2. Therefore, the expression representing the minimum amount of paint needed for one block is 6b^2.

b. If the production team decides to use two coats of paint for each block, the total surface area that needs to be covered with paint would be doubled. Therefore, the expression representing the minimum amount of paint needed for one block with edge b is 2 * 6b^2, which simplifies to 12b^2.

c. If a can of paint covers 60in^2 and the production team wants to use two coats of paint for each block, we can set up an inequality. The total surface area that needs to be covered with two coats is 12b^2 (from part b). So, the inequality would be: 12b^2 ≤ 60. Simplifying this inequality, we find that the maximum length of edge b, in inches, is √(60/12), which is approximately 2.58 inches.