Question

A toy is in the shape of a square pyramid of base edge 18 centimetres and height 12 centimetres. What is the total cost of painting 500 such toys at 120 rupees per square metre ?

Hint:

For problems involving cost of painting or covering, first determine whether to use Lateral Surface Area (LSA) or Total Surface Area (TSA) based on the context. Then, calculate the total area for all items and perform the unit conversion *before* multiplying by the cost to avoid large numbers and potential errors.

Answer 1

We need to find the total cost of painting 500 identical square pyramids. "Painting" usually refers to the exposed surface area. For a toy that sits on its base, this typically means the Lateral Surface Area (LSA). We will calculate the cost based on the LSA.

- Lateral Surface Area (LSA) of a square pyramid = 2 × a × l, where a is the base edge and l is the slant height.
- The slant height (l) is found using the pyramid's height (h) and half the base edge (a/2): l² = h² + (a/2)².
- Unit conversion: 1 m² = 10000 cm².

1. Find the slant height (l).
Given: Base edge, a = 18 cm, and Height, h = 12 cm.
Half base edge, a/2 = 18/2 = 9 cm.
Using the Pythagorean theorem:
l = √(h² + (a/2)²) = √(12² + 9²) = √(144 + 81) = √(225) = 15 cm 2. Calculate the LSA of one toy.
LSA = 2 × a × l = 2 × 18 × 15 = 540 cm² 3. Calculate the total area to be painted for 500 toys in m².
Total LSA in cm² = LSA of one toy × 500 = 540 × 500 = 270000 cm².
Convert this area to square metres:
Total LSA in m² = (270000)/(10000) = 27 m².

4. Calculate the total cost.
Cost per square metre = 120 rupees.
Total Cost = Total LSA in m² × Cost per m²
Total Cost = 27 × 120 = 3240 rupees Note:
Some answer keys state 32400 rupees. This would only be correct if the cost were 1200 rupees per square metre, suggesting a typo in the question's cost value. Based on the provided data, the correct cost is 3240 rupees.

The total cost of painting the lateral surface of 500 toys is 3240 rupees.