Question

Harrison works at a factory that makes paper cups for water coolers. He calculated the outer surface area of each hollow cup as 17.9 square inches. What is the approximate slant height of the cup?

Answer 1

We can use the formula for the lateral surface area of a cone to find the slant height:

Lateral surface area = πrℓ, where r is the radius and ℓ is the slant height.

Since the paper cup is hollow, the lateral surface area is equal to the outer surface area of the cup, which is given as 17.9 square inches. The radius of the cup is half the diameter, which we do not know, so let's call it d:

r = d/2

We also know that the lateral surface area is given by:

17.9 = πrℓ

Substituting r = d/2, we get:

17.9 = π(d/2)ℓ

Simplifying, we get:

ℓ = (2*17.9)/(πd)

Using an approximation of π = 3.14, we can calculate:

ℓ ≈ (2*17.9)/(3.14d) = 11.40/d

Since we do not have any information about the diameter of the paper cup, we cannot calculate the exact slant height.