Question

Anniston has a sink that is shaped like a half-sphere. plz help gets brainy

Answer 1

Part A)
`167\ cups`

Part B)
`10\ cups`

Explanation:

Part A)

we know that

The volume of the sink is

`V=(2,000)/(3)\pi\ in^(3)`

step 1

Find the volume of the cylindrical cup

The volume is equal to

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

we have

`r=2/2=1\ in` ----> the radius is half the diameter

`h=4\ in`

substitute the values

`V=\pi (1)^(2) (4)`

`V=4\pi\ in^(3)`

step 2

To find the number of cups of water, divide the total volume of the sink by the volume of the cylindrical cup

`((2,000)/(3)\pi)/(4\pi)=(2,000)/(12)=166.67\ cups`

Round to the nearest whole number

`167\ cups`

Part B)

we know that

The volume of the sink is

`V=(2,000)/(3)\pi\ in^(3)`

step 1

Find the volume of the cylindrical cup

The volume 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)`

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

step 2

To find the number of cups of water, divide the total volume of the sink by the volume of the cylindrical cup

`((2,000)/(3)\pi)/(72\pi)=(2,000)/(216)=9.26\ cups`

Round to the nearest whole number (Round up)

`10\ cups`