Question

The costume department of a theatre company is making cone-shaped hats for a play set in medieval times. Each hat will be covered with satin over its entire lateral surface area. The slant height of each hat will remain constant at 20 inches, but the radius of the base will vary to accommodate different head sizes. Using 3.14 for π, the lateral area of the hat can be expressed as a function. A. y = 20πx B. y = 3.14x C. y = 40πx D. y = 10x

Answer 1

The lateral area of the cone-shaped hats can be represented by the function y = 20πx.

The correct option is A.

Step-by-step explanation:

The lateral surface area of a cone can be calculated using the formula LSA = πrℓ, where r is the radius of the base and ℓ is the slant height. In this case, the slant height is constant at 20 inches. So, the lateral area can be expressed as LSA = 20πr. Therefore, the function that represents the lateral area of the cone-shaped hats is y = 20πx, where y represents the lateral area and x represents the radius of the base.

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