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?
For a can with both ends closed, Area reqd. = 2¡Çrh + 2¡Çr^2 where r=6,h=4 and assume ¡Ç=22/7, A=2640/7 sq in.
If one end of the can is open then A=2¡Çrh + ¡Çr^2 = 264 sq in.
Area of circle = πr^2
Multiply by 2 to get top and bottom.
Circumference = 2πr
Area of side = 4 *2πr
Combine the data.
376.8 in.2
To find the surface area of the aluminum can, we need to calculate the area of the curved surface (excluding the top and bottom) and the area of the circular top and bottom.
1. Curved Surface Area:
The curved surface of the can can be thought of as the lateral surface area of a cylinder. The formula for the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2 * π * r * h,
where π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, the radius (r) of the can is 6 in and the height (h) of the can is 4 in. Plugging these values into the formula:
Curved Surface Area = 2 * π * 6 * 4 = 48π square inches.
2. Circular Top and Bottom Area:
The top and bottom of the can can be thought of as two circles. The formula for the area of a circle is given by:
Area of Circle = π * r^2,
where r is the radius of the circle.
In this case, the radius (r) of the can is 6 in. Plugging this value into the formula:
Area of Circle = π * 6^2 = 36π square inches.
3. Total Surface Area:
To find the total surface area of the can, we add the curved surface area and the area of the top and bottom:
Total Surface Area = Curved Surface Area + 2 * Area of Circle
= 48π + 2 * 36π
= 48π + 72π
= 120π square inches.
So, to make the can, we would need 120π square inches of aluminum.