Answer:
Part A) [tex]167\ cups[/tex]
Part B) [tex]10\ cups[/tex]
Step-by-step explanation:
Part A)
we know that
The volume of the sink is
[tex]V=\frac{2,000}{3}\pi\ in^{3}[/tex]
step 1
Find the volume of the cylindrical cup
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=2/2=1\ in[/tex] ----> the radius is half the diameter
[tex]h=4\ in[/tex]
substitute the values
[tex]V=\pi (1)^{2} (4)[/tex]
[tex]V=4\pi\ in^{3}[/tex]
step 2
To find the number of cups of water, divide the total volume of the sink by the volume of the cylindrical cup
[tex](\frac{2,000}{3}\pi)/(4\pi)=\frac{2,000}{12}=166.67\ cups[/tex]
Round to the nearest whole number
[tex]167\ cups[/tex]
Part B)
we know that
The volume of the sink is
[tex]V=\frac{2,000}{3}\pi\ in^{3}[/tex]
step 1
Find the volume of the cylindrical cup
The volume 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)[/tex]
[tex]V=72\pi\ in^{3}[/tex]
step 2
To find the number of cups of water, divide the total volume of the sink by the volume of the cylindrical cup
[tex](\frac{2,000}{3}\pi)/(72\pi)=\frac{2,000}{216}=9.26\ cups[/tex]
Round to the nearest whole number (Round up)
[tex]10\ cups[/tex]
