Question

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

Answer 1

Part a)
`42\ cups`

Part b)
`15\ cups`

Step-by-step explanation:we know that

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

`V=3,000\pi \ in^(3)`

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

`V=\pi r^(2)h`

we have

`r=6/2=3\ in` ----> the radius is half the diameter

`h=8\ in`

substitute the values

`V=\pi (3)^(2)(8)=72\pi\ in^(3)`

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

`(3,000\pi)/(72\pi) =41.67\ cups`

Round to the nearest whole number

`41.67=42\ cups`

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

`V=\pi r^(2)h`

we have

`r=10/2=5\ in` ----> the radius is half the diameter

`h=8\ in`

substitute the values

`V=\pi (5)^(2)(8)=200\pi\ in^(3)`

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

`(3,000\pi)/(200\pi) =15\ cups`