I'm so confused... I've always been good at math but this year I'm just not getting it. But I know i can I always get help and a REAL explanation from the people on here so...

A steel drum in the shape of a right circular cylinder required to have a volume of 100 cubic feet.
(a) Express the amount A of material required to the make the drum as a function of the radius "r" to the cylinder.
(b) How much material is required if the drum is of radius 3 feet?
(c) Of radius 4 feet?
(d) Of radius 5 feet?

I'm so confused, I don't even know where to start!!!

They want the surface area of the cylinder, including top and bottom. The two ends have a combined area of 2 pi r^2. The side wall area is 2 pi r L, where L is the length. The relationship between L and r is

pi r^2 L = 100

Write the equation for A, using
L = 100/(pi r^2) to eliminate L

Then plug in the numbers.

Thanks! I didn't realize it could be so easy!

I understand that you're feeling confused about this math problem, but I'll do my best to help you understand it step by step.

Let's start by breaking down the problem into smaller parts.

(a) Expressing the amount A of material required to make the drum as a function of the radius "r" of the cylinder.
To find the amount of material required, we need to calculate the surface area of the cylinder. The formula for the surface area of a cylinder is 2πr^2, where π is a constant approximately equal to 3.14 and r is the radius of the cylinder.

So, the amount of material A required to make the drum can be expressed as a function of the radius r using the formula A = 2πr^2.

(b) Now, let's find how much material is required if the drum has a radius of 3 feet.
We can substitute the radius value (r = 3) into the function A = 2πr^2 to calculate the amount of material required.

A = 2π(3^2) = 2π(9) = 18π square feet of material.

(c) Let's find how much material is required if the drum has a radius of 4 feet.
Using the same process as above but substituting r = 4 into the function:

A = 2π(4^2) = 2π(16) = 32π square feet of material.

(d) Lastly, let's find how much material is required if the drum has a radius of 5 feet.
Using the same process as above but substituting r = 5 into the function:

A = 2π(5^2) = 2π(25) = 50π square feet of material.

To summarize:
(b) The drum with a radius of 3 feet requires 18π square feet of material.
(c) The drum with a radius of 4 feet requires 32π square feet of material.
(d) The drum with a radius of 5 feet requires 50π square feet of material.

Remember, understanding math problems comes with practice and breaking them down into smaller steps. I hope this explanation helps simplify the problem for you!