Question

chapter 5 practice

1. a fashion designer is designing an a - line skirt (in the shape of an a). the goal of the fashion designer is to cut each skirt from one piece of cloth, which means the skirt will have only one seam. this makes a cone shape, minus the vertex of the cone. using the dimensions given in the diagram, determine the amount of cloth needed for each skirt.

a. develop a plan. how will you determine surface area of the skirt using the dimensions given?
b. determine the amount of cloth in the skirt (the surface area). round to two decimal places.

Explanation:

Step1: Recall the formula for the lateral - surface area of a frustum of a cone

The lateral - surface area of a frustum of a cone is $A=\pi l(R + r)$, where $l$ is the slant height, $R$ is the radius of the larger base, and $r$ is the radius of the smaller base.

Step2: Identify the values of $R$, $r$, and $l$

From the diagram, the radius of the larger base $R=\frac{0.65}{2}=0.325$ m, the radius of the smaller base $r = \frac{0.31}{2}=0.155$ m, and the slant height $l = 0.52$ m.

Step3: Substitute the values into the formula

$A=\pi\times0.52\times(0.325 + 0.155)$
$A=\pi\times0.52\times0.48$
$A = 0.2496\pi$

Step4: Calculate the value and round

$A\approx0.78$ m²

Answer:

a. Plan: Use the formula for the lateral - surface area of a frustum of a cone $A=\pi l(R + r)$, where $l$ is the slant height, $R$ is the radius of the larger circular base of the frustum, and $r$ is the radius of the smaller circular base of the frustum. Identify the values of $l$, $R$, and $r$ from the given diagram and substitute them into the formula.
b. $0.78$ m²