Michael has a sink that is shaped like a half-sphere. the sink has a volume of 3000 3 in3. one day, his sink is clogged. he has to use one of two cylindrical cups to scoop the water out of the sink. the sink is completely full when michael begins scooping. (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? round the number of scoops to the nearest whole number. (b) one cup has a diameter of 10 in. and a height of 8 in. how many cups of water must he scoop out of the sink with this cup to empty it? round the number of scoops to the nearest whole number

Part a)

Part b)

Step-by-step explanation:we know that

The volume of the sink (half sphere) is equal to

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

we have

----> the radius is half the diameter

substitute the values

To find the number of cups divide the total volume of the sink by the volume of the cylinder

Round to the nearest whole number

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

we have

----> the radius is half the diameter

substitute the values

To find the number of cups divide the total volume of the sink by the volume of the cylinder

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph