Question

A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.6 inch and a height of 2.4 inches. How many total square inches of gift wrap will the makeup artist need to wrap 4 lipsticks? Leave the answer in terms of π.

Answer 1

Explanation:

Total surface area of a cylinder = 2πr(r + h)

2 π (.6) (.6 + 2.4)

2 π .6 (3)

1.2π (3)

3.6 π square inches

Mulitply by four for four lipsticks:

3.6π × 4 = 14.4π sq inches

Answer 2

The formula for the surface area of a cylinder is:

S = 2πrh + 2πr^2

where S is the total surface area, r is the radius of the base, and h is the height.

For one lipstick, the surface area is:

S = 2π(0.6)(2.4) + 2π(0.6)^2

S = 2.88π + 0.72π

S = 3.6π

To wrap 4 lipsticks, we need to multiply this surface area by 4:

S = 4(3.6π)

S = 14.4π

Therefore, the makeup artist will need approximately 14.4π square inches of gift wrap to wrap 4 lipsticks.