Question

makes a cone shape. using the dimensions given in 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?
r = \frac{0.65}{2}=0.325m
r = \frac{0.31}{2}=0.155m
l = 0.52
b. determine the amount of cloth in the skirt (the surface area). round to two decimal places.

Explanation:

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

The lateral - surface area of a cone is given by $A = \pi rl$, where $r$ is the radius of the base of the cone and $l$ is the slant height of the cone.

Step2: Identify the values of $r$ and $l$ from the problem

From the problem, assume the slant height $l = 0.52$ m and the radius of the base $r=0.155$ m (as calculated in the given work).

Step3: Calculate the surface area

Substitute the values of $r$ and $l$ into the formula: $A=\pi\times0.155\times0.52$.
$A = 0.155\times0.52\pi=0.0806\pi\approx 0.25$ m² (rounded to two decimal places).

Answer:

Approximately $0.25$ m²