Question

Chocolates are packaged in boxes that measure 18 cm by 20 cm by 6 cm. A larger box is being designed by increasing the length, width, and height of the smaller box by the same length so that the volume is at least 5280 cm^3 cm. What are the minimum dimensions of the large box?

Answer 1

To find the minimum dimensions of the large box, increase the length, width, and height of the small box by the same length. Set the volume of the large box equal to 5280 cm³ and solve for x to determine the minimum dimensions.

Step-by-step explanation:

To find the minimum dimensions of the large box, we need to increase the length, width, and height of the smaller box by the same length. The volume of the smaller box can be calculated by multiplying its length, width, and height: 18 cm * 20 cm * 6 cm = 2160 cm³. We want the volume of the large box to be at least 5280 cm³. Let's assume the length we need to increase by is x cm, then the volume of the large box can be calculated as (18 cm + x) * (20 cm + x) * (6 cm + x). Setting this equal to 5280 cm³, we can solve for x to find the minimum dimensions of the large box.