Question

Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 3000

(pie symbol) in3
. One day, her
3
sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is
completely full when Carissa begins scooping.
(a) One cup has a diameter of 5 in. and a height of 6 in. How many cups of water must Carissa scoop out
of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
Show all your work.
(b) One cup has a diameter of 6 in. and a height of 6 in. How many cups of water must she scoop out of
the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
WORTH 20 POINTS

Answer 1

a) 80
b) 56

Explanation:

a) Calculate the volume of the the cup using volume of cylinder equation:
`V = \pi r^(2) h`

Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches (
`in^3`).
You're given diameter, so use equation
`d/2 = r` to find radius.
Substituting these equations will give you:
`V = \pi (d/2)^2 h`
However, the given volume of the sink is 3000
`\pi`, meaning that you should modify your results to match this value. Do not substitute
`\pi` for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5
`\pi`
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:

`Vsink / V cup =` # of cups.
Note the the
`\pi` will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.