Mr. Sandeep was placing an order with his carpenter to make wooden boxes to pack his cotton toys which were to be delivered to his friend. Sandeep wanted 2 types of boxes. The larger one with a dimension of 25cm x 20cm x 5cm and the smaller box with a dimension of 15cm x 12cm x 5cm. Sandeep also told the carpenter that 5% of total surface area is required as extra to cover the overlaps. If the cost of the wood is Rs.4/- cmz, the cost of wood required for supplying 250 boxes of each type would be Rs. ______.[Note:-D0 NOT include spaces in your answer)
To determine the cost of wood required for 250 boxes of each type, we need to calculate the total surface area of both types of boxes, including the extra 5% for overlaps. 1. Surface Area Calculation: - Larger Box: Dimensions: 25 cm x 20 cm x 5 cm Surface Area = 2(lw + lh + wh) \[ = 2(25 \times 20 + 25 \times 5 + 20 \times 5) \] \[ = 2(500 + 125 + 100) \] \[ = 2 \times 725 \] \[ = 1450 \text{ cm}^2 \] Including 5% extra: \[ = 1450 \times 1.05 = 1522.5 \text{ cm}^2 \] - Smaller Box: Dimensions: 15 cm x 12 cm x 5 cm Surface Area = 2(lw + lh + wh) \[ = 2(15 \times 12 + 15 \times 5 + 12 \times 5) \] \[ = 2(180 + 75 + 60) \] \[ = 2 \times 315 \] \[ = 630 \text{ cm}^2 \] Including 5% extra: \[ = 630 \times 1.05 = 661.5 \text{ cm}^2 \] 2. Total Surface Area for 250 Boxes of Each Type: - Total for larger boxes: \[ = 250 \times 1522.5 = 380625 \text{ cm}^2 \] - Total for smaller boxes: \[ = 250 \times 661.5 = 165375 \text{ cm}^2 \] - Total Surface Area: \[ = 380625 + 165375 = 546000 \text{ cm}^2 \] 3. Cost Calculation: Cost of wood = Total Surface Area \(\times\) Cost per cm\(^2\) \[ = 546000 \times 4 = 2184000 \text{ Rs} \] Thus, the cost of the wood required for supplying 250 boxes of each type is Rs. 2184000.
