Answer:
[tex]Scoops = 12[/tex] --- cup 1
[tex]Scoops = 5[/tex] --- cup 2
Step-by-step explanation:
Given
Hemisphere
[tex]Volume = \frac{4500\pi}{3}\ in^3[/tex]
Cup 1
[tex]Height = 14\ in[/tex]
[tex]Diameter = 6\ in[/tex]
Cup 2
[tex]Height = 12\ in[/tex]
[tex]Diameter = 10\ in[/tex]
Required: How many scoop of each?
For cup 1
Calculate the volume
[tex]Volume = \pi r^2h[/tex]
Where
[tex]h = 14[/tex]
[tex]r = \frac{1}{2} * 6 = 3[/tex]
[tex]Volume = \pi r^2h[/tex]
[tex]Volume = \pi * 3^2 * 14[/tex]
[tex]Volume = \pi * 126[/tex]
[tex]Volume = 126\pi[/tex]
Divide the volume of the hemisphere by the calculated volume of cup 1
[tex]Scoops = \frac{4500\pi}{3} / 126\pi[/tex]
[tex]Scoops = \frac{4500\pi}{3} * \frac{1}{126\pi}[/tex]
[tex]Scoops = \frac{1500\pi}{1} * \frac{1}{126\pi}[/tex]
[tex]Scoops = \frac{1500\pi}{126\pi}[/tex]
[tex]Scoops = 12[/tex] --- approximated
For cup 2
Calculate the volume
[tex]Volume = \pi r^2h[/tex]
Where
[tex]h =12[/tex]
[tex]r = \frac{1}{2} * 10 = 5[/tex]
[tex]Volume = \pi r^2h[/tex]
[tex]Volume = \pi * 5^2 * 12[/tex]
[tex]Volume = \pi * 300[/tex]
[tex]Volume = 300\pi[/tex]
Divide the volume of the hemisphere by the calculated volume of cup 2
[tex]Scoops = \frac{4500\pi}{3} / 300\pi[/tex]
[tex]Scoops = \frac{4500\pi}{3} * \frac{1}{300\pi}[/tex]
[tex]Scoops = \frac{1500\pi}{1} * \frac{1}{300\pi}[/tex]
[tex]Scoops = \frac{1500\pi}{300\pi}[/tex]
[tex]Scoops = 5[/tex]
