Question

communication (4 marks)

1. a company is designing a can that needs a label covering the entire surface area of the cylinder. if the can has a radius of 5 cm and a height of 15 cm, explain why the surface area formula is important in real - world applications like this.

Explanation:

The surface area formula for a cylinder ($SA = 2\pi r^{2}+2\pi rh$) is crucial here. The label covering the entire surface area of the can (a cylinder) requires knowing the amount of material (label - paper) needed. The formula calculates the total area of the two circular bases ($2\pi r^{2}$) and the lateral (curved) surface area ($2\pi rh$). In real - world applications like designing this can, knowing the surface area helps in:

• Cost Estimation: Determining the cost of the label material. If the cost per unit area of the label paper is known, multiplying it by the surface area (calculated using the formula) gives the total cost for the labels of all cans.
• Material Sourcing: Knowing how much material (in terms of area) is required to produce the labels, which helps suppliers and manufacturers plan their inventory and production processes.
• Quality Control: Ensuring that the label fits perfectly on the can. If the surface area is miscalculated, the label may be too small (not covering the can completely) or too large (wasting material).

Answer:

The surface area formula for a cylinder is important in this real - world application (designing a can label) for cost estimation (of label material), material sourcing (planning inventory based on area requirements), and quality control (ensuring proper fit of the label on the can).