Answer:
the amount of metal required to make the can is 352.8π square centimeters.
Explanation:
To calculate the amount of metal required to make the can, we need to find the surface area of the can.
The can consists of two circular ends (top and bottom) and a cylindrical body.
1. Surface Area of the Circular Ends:
The circular ends can be considered as two circles. The surface area of each circular end can be calculated using the formula for the area of a circle:
A_end = πr^2
Given the diameter of the can is 14 cm, the radius (r) is half the diameter, so r = 14 cm / 2 = 7 cm.
A_end = π * 7^2 = 49π cm^2 (for each circular end)
2. Surface Area of the Cylindrical Body:
The cylindrical body of the can can be represented as a rectangle that is rolled into a cylinder. The surface area of the cylindrical body can be calculated using the formula for the lateral surface area of a cylinder:
A_body = 2πrh
Given the height (h) of the can is 18.2 cm and the radius (r) is 7 cm, we can calculate the surface area of the cylindrical body:
A_body = 2π * 7 * 18.2 = 254.8π cm^2
3. Total Surface Area:
To calculate the total surface area of the can, we add the surface areas of the circular ends and the cylindrical body:
Total Surface Area = 2 * A_end + A_body
= 2 * 49π + 254.8π
= 98π + 254.8π
= 352.8π cm^2
Therefore, the amount of metal required to make the can is 352.8π square centimeters.