Answer:
Part a) [tex]42\ cups[/tex]
Part b) [tex]15\ cups[/tex]
Step-by-step explanation:we know that
The volume of the sink (half sphere) is equal to
[tex]V=3,000\pi \ in^{3}[/tex]
Part a) One cup has a diameter of 6 in. and a height of 8 in. How many cups of water must Michael scoop out of the sink with this cup to empty it?
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter
[tex]h=8\ in[/tex]
substitute the values
[tex]V=\pi (3)^{2}(8)=72\pi\ in^{3}[/tex]
To find the number of cups divide the total volume of the sink by the volume of the cylinder
[tex]\frac{3,000\pi}{72\pi} =41.67\ cups[/tex]
Round to the nearest whole number
[tex]41.67=42\ cups[/tex]
Part b) One cup has a diameter of 10 in. and a height of 8 in. How many cups of water must Michael scoop out of the sink with this cup to empty it?
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
[tex]h=8\ in[/tex]
substitute the values
[tex]V=\pi (5)^{2}(8)=200\pi\ in^{3}[/tex]
To find the number of cups divide the total volume of the sink by the volume of the cylinder
[tex]\frac{3,000\pi}{200\pi} =15\ cups[/tex]
