Question

Conical containers are often used for selling popcorn or snow cones. To construct a cone, a sector is cut out from a circle, and then the cut edges are joined. In the diagram below, the dotted lines represent the cuts. Find the area of the remaining sector that would be needed to make this cone with the given dimensions (cone height: 24cm, cone radius: 18cm, cone circumference 113.1cm).

Answer 1

Solution:

The given dimensions are

$\begin{gathered} r=18cm \\ C=131.1cm \end{gathered}$

Step 1:

We will calculate the angle of the sector

To do this, we will use the formula below

$A=\frac{\theta}{360}\times\pi R^2$

By substituting the values, we will have

$\begin{gathered} R^2=18^2+24^2 \\ R^2=324+576 \\ R^2=900 \\ R=\sqrt{900} \\ R=30 \end{gathered}$$\begin{gathered} \theta=\frac{C}{R}=\frac{113.1}{30} \\ A=\frac{\theta}{2\pi}\times\pi R^2 \\ A=\frac{113.1}{\frac{30}{2}}\times30^2 \\ A=\frac{113.1}{60}\times900 \\ A=1696.5cm^2 \end{gathered}$

Hence,

The final answer is

$\Rightarrow A=1,696.5cm^2$