Answer:
[tex]d = 787.81cm^3[/tex]
Step-by-step explanation:
Given
See attachment for the containers
Required
The difference in the amount of snow cone they hold
The amount they hold is determined by calculating the volume of the containers.
The traditional snow cone has the following dimension
Shape: Cone
[tex]r=4cm[/tex] --- radius
[tex]h = 13cm[/tex] --- height
The volume is calculated as:
[tex]Volume = \frac{1}{3} \pi r^2h[/tex]
So, we have:
[tex]V_1 = \frac{1}{3} \pi * 4^2 * 13[/tex]
[tex]V_1 = \frac{208}{3} \pi[/tex]
The snow cone in a cup has the following dimension
Shape: Cylinder
[tex]r=8cm[/tex] --- radius
[tex]h = 5cm[/tex] --- height
The volume is calculated as:
[tex]Volume = \pi r^2h[/tex]
So, we have:
[tex]V_2 = \pi *8^2 * 5[/tex]
[tex]V_2 = \pi *320[/tex]
[tex]V_2 = 320\pi[/tex]
The difference (d) in the amount they hold is:
[tex]d = V_2 - V_1[/tex]
[tex]d = 320\pi - \frac{208\pi}{3}[/tex]
Take LCM
[tex]d = \frac{3*320\pi -208\pi}{3}[/tex]
[tex]d = \frac{960\pi -208\pi}{3}[/tex]
[tex]d = \frac{752\pi}{3}[/tex]
Take [tex]\pi = 22/7[/tex]
[tex]d = \frac{752}{3} * \frac{22}{7}[/tex]
[tex]d = \frac{752 * 22}{3*7}[/tex]
[tex]d = \frac{16544}{21}[/tex]
[tex]d = 787.81cm^3[/tex]
