In this activity, you'll create a polynomial equation to design a cylindrical silo based on certain dimensions. Sometimes when modeling real-world situations, you first need to find the factors of the polynomial equation. These factors, when multiplied
together, will form the polynomial equation that represents the situation. You can then use that equation to answer questions about the situation.
You'll see such an example in this activity. Read the scenario below, and then answer the questions.
Imagine you're a farmer and are planning to build a cylindrical silo to hold your harvested grain. For your farm's logo to completely fit on the silo,
you need the silo to be 5 feet taller than its diameter. You also need to design the silo so it will hold a specific amount of grain.
Part A
Let d represent the diameter of the silo. Write expressions to represent the radius and height of the silo.