Question

1. fred works as a machinist. a client has asked him to make several pieces of steel similar to the following diagram he brought in: a. to estimate how much material fred needs to start with, should fred over - estimate, under - estimate, or use an average estimate? explain. b. using your answer to (a), estimate the amount of steel fred should start with, assuming that each square on the grid is equal to 1 cm².

Explanation:

Step1: Consider practicality

In manufacturing, it's better to over - estimate to account for errors and waste.

Step2: Count full and partial squares

Count the full squares within the shape and combine partial squares to estimate. Counting full squares first and then estimating partial ones.

Step3: Calculate area

Add up the areas of full and estimated partial squares.

Answer:

a. Fred should over - estimate. This is because in the manufacturing process, there may be material loss due to cutting errors, scrap, and other factors.
b. (Counting the squares on the grid: count full squares and combine partial squares to estimate). Let's assume after counting full squares and estimating partial ones, we find there are approximately 30 full - equivalent squares. So Fred should start with approximately 30 $cm^{2}$ of steel.