Large pizza are sold in cardboard boxes when closed the boxes measure 40cm by 40cm by 2.5cm and are cuboid. The company think it could use the same net but reduce the dimensions to 38cm by 38cm by 2cm. Sides and flaps all have a width of 2.5cm. Beth is asked to calculate the percentage reduction in cardboard if the smaller boxes are used. What answer should Beth get?.

To find the percentage reduction in cardboard, we need to compare the area of the original box and the area of the smaller box. The area of a cuboid box is given by the formula: A = 2(lw + lh + wh) where l is the length, w is the width, and h is the height of the box. The area of the original box is: A_1 = 2(40 \times 40 + 40 \times 2.5 + 40 \times 2.5) A_1 = 2(1600 + 100 + 100) A_1 = 2(1800) A_1 = 3600 \text{ cm}^2 The area of the smaller box is: A_2 = 2(38 \times 38 + 38 \times 2 + 38 \times 2) A_2 = 2(1444 + 76 + 76) A_2 = 2(1596) A_2 = 3192 \text{ cm}^2 The percentage reduction in cardboard is given by the formula: P = \frac{A_1 - A_2}{|A_1|} \times 100 where A_1 is the original area and A_2 is the new area. Plugging in the values, we get: P = \frac{3600 - 3192}{|3600|} \times 100 P = \frac{408}{3600} \times 100 P = 0.113 \times 100 P = 11.3\% Therefore, Beth should get 11.3% as the answer. This means that the smaller boxes use 11.3% less cardboard than the original boxes.