An aluminum cylindrical juice can has a height of 4 in. and a radius of 6 in. How many square

inches of aluminum are needed to make the can?

Visualize a can, cut off the circles at the top and bottom, and cut open the remaining "sleeve".

Don't you now have 1 rectangle and 2 equal circles?
Find the areas of each and add them up

(hint: the length of the rectangle is the circumference of the circle)

To find the total surface area (in square inches) of the cylindrical juice can, we need to consider both the surface area of the circular top and bottom (the bases) and the surface area of the curved part (the lateral area).

Let's break it down step by step:

1. Calculate the surface area of the bases:
- The base of the can is a circle, so we can find the area using the formula: A = π * r^2
where A is the area and r is the radius.
- For the top and bottom bases, we have two circles, so the total area of the bases is: 2 * (π * r^2)

2. Calculate the lateral area of the curved part:
- The lateral area of a cylinder is given by the formula: A = 2πrh
where A is the lateral area, π is pi (approximately 3.14159), r is the radius, and h is the height.

3. Add the area of the bases and the lateral area together to find the total surface area:
- Total Surface Area = 2 * (π * r^2) + 2πrh

Now let's substitute the values given in the problem:

- Radius (r) = 6 in
- Height (h) = 4 in

Calculating step by step:

1. Calculate the surface area of the bases:
- Area of each base = π * r^2 = 3.14159 * 6^2 ≈ 113.097 in^2
- Total area of the bases = 2 * 113.097 = 226.194 in^2

2. Calculate the lateral area of the curved part:
- Lateral Area = 2πrh = 2 * 3.14159 * 6 * 4 ≈ 150.796 in^2

3. Calculate the total surface area:
- Total Surface Area = 2 * (π * r^2) + 2πrh = 2 * 113.097 + 150.796 ≈ 376.986 in^2

Therefore, approximately 376.986 square inches of aluminum are needed to make the cylindrical juice can.