Question

Show your solution. A canned drink will be made using 40 in² of aluminum. Let r be the radius of the can and let h be the height. Define the function in terms of r that can represent the volume of the can.

Answer 1

To find the volume of the can, we use the formula for the surface area of a cylinder and solve for the height in terms of the radius. Then, we substitute the height into the formula for the volume of a cylinder to get the function in terms of r.

Step-by-step explanation:

To find the volume of the can, we first need to find the radius and height of the can using the given information. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. Since we are given the area of the aluminum, we can use the formula for the surface area of a cylinder, which is A = 2πrh + 2πr^2. We know that the surface area is 40 in², so we have 40 = 2πrh + 2πr^2. Now we can solve this equation for h in terms of r.

Next, we substitute the value of h in terms of r into the volume formula. V = πr^2h becomes V = πr^2(20/πr + 2r) which simplifies to V = 20r + 2πr^3. This is the function in terms of r that represents the volume of the can.

Learn more about Volume of a Cylinder