10. you are scooping popcorn from a gigantic bag and pouring it into a paper cone. the scoop (cylinder) has radius of 2 in and a height of 3 in. the paper cone has a radius of 3 in. and a height of 10 in. how many scoops do you need to fill a cone with popcorn? ____________ (think about the rounding)

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Accepted Answer

# Explanation:
## Step1: Calculate the volume of the cylinder (scoop)
The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 2$ in and $h=3$ in.
$$
\begin{align*}
V_{cylinder}&=\pi\times(2)^{2}\times3\
&=\pi\times4\times 3\
& = 12\pi\space\text{in}^{3}
\end{align*}
$$
## Step2: Calculate the volume of the cone
The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Given $r = 3$ in and $h = 10$ in.
$$
\begin{align*}
V_{cone}&=\frac{1}{3}\pi\times(3)^{2}\times10\
&=\frac{1}{3}\pi\times9\times10\
&=30\pi\space\text{in}^{3}
\end{align*}
$$
## Step3: Find the number of scoops
Let $n$ be the number of scoops. Then $n=\frac{V_{cone}}{V_{cylinder}}$
$$
\begin{align*}
n&=\frac{30\pi}{12\pi}\
&=\frac{30}{12}\
& = 2.5
\end{align*}
$$
Since we can't have a fraction of a scoop when filling (we need to completely fill the cone), we round up.

# Answer:
$3$

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Question

Explanation:

Step1: Calculate the volume of the cylinder (scoop)

Step2: Calculate the volume of the cone

Step3: Find the number of scoops

Answer: