To find the amount of wrapping paper needed to cover a cylindrical box, we need to find the lateral area and the area of the two circular bases, and then add them together.
The formula for the lateral area of a cylinder is L = 2πrh, where r is the radius and h is the height. So, in this case, the lateral area is:
L = 2 × 3.14 × 7 × 6 = 263.04 square units
The formula for the area of a circle is A = πr^2. So, in this case, the area of one circular base is:
A = 3.14 × 7^2 = 153.86 square units
Since there are two circular bases, the total area of the two bases is:
2A = 2 × 153.86 = 307.72 square units
To find the total amount of wrapping paper needed, we add the lateral area and the area of the two circular bases:
Total area = L + 2A = 263.04 + 307.72 = 570.76 square units
Therefore, we need 570.76 square units of wrapping paper to cover the cylindrical box