A pastry chef started producing cakes in the shape of a right circular cylinder, with the radius of the base varying between 12 cm and 16 cm and height of 6 cm. These cakes should be packaged in boxes with the shape of a right prism with a square base, so that it is possible to accommodate the cake inside and still have at least 1 cm of distance remaining between the cake and the internal surfaces of the box, lateral and upper. He originally has boxes in the intended format, whose internal dimensions are 14 cm for the length of the side of the base and 7 cm in height, which do not meet his needs. Therefore, he will buy new boxes, with the same format as the original boxes, but with a larger length of the side of the base, that are suitable for packaging all types of cakes he produces. The edge of the base of the new boxes should be, at minimum, how many centimeters larger than that of the original boxes? (A) 4 (B) 12 (C) 16 (D) 18 (E) 20
A pastry chef started producing cakes in the shape of a right circular cylinder, with the radius of the base varying between 12 cm and 16 cm and height of 6 cm. These cakes should be packaged in boxes with the shape of a right prism with a square base, so that it is possible to accommodate the cake inside and still have at least 1 cm of distance remaining between the cake and the internal surfaces of the box, lateral and upper. He originally has boxes in the intended format, whose internal dimensions are 14 cm for the length of the side of the base and 7 cm in height, which do not meet his needs. Therefore, he will buy new boxes, with the same format as the original boxes, but with a larger length of the side of the base, that are suitable for packaging all types of cakes he produces.
The edge of the base of the new boxes should be, at minimum, how many centimeters larger than that of the original boxes?\\
(A) 4\\
(B) 12\\
(C) 16\\
(D) 18\\
(E) 20