Question

Kim also has a sink that is shaped like a half-sphere. The sink has a volume of 4000/3 π in3. One day, her 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 Kim begins scooping. a) One cup has a diameter of 6in. and a height of 10in. How many cups of water must Kim 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 10in. and a height of 10in. 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

Answer 1

A. 44 times

B. 16 times.

Explanation:

We know the volume of the sink, now we need to find the volume of the cup(s) she's using to empty it out. to find out how many scoops she'll have to do.

We'll assume she can actually empty it all, even if it's unlikely he can scoop the last 5%-10% of it due to the shapes/sizes of the sink and the cup. We'll also assume she completely fills the cup (which is impossible due to angles).

The volume of the sink is 4000/3 π cubic inches

a - Conical cup, diameter 6 inches (radius = 3), height: 10 inches.

We remember the volume of a cone is found using this formula:

V = (π r² h) / 3

So, we have:

V = (π * 3² * 10) / 3 = 90 π / 3

So, how many times does Kim has to scoop (S):

`S = (4000 \pi /3 )/(90 \pi /3 ) = 44.44`

Of course, she can't scoop 0.44 times... Normally we would round it up, but the question says to round it to the nearest whole number.

So, Kim will have to scoop 44 times with this first cup.

b - Conical cup, diameter 10 inches (radius = 5), height: 10 inches.

We remember the volume of a cone is found using this formula:

V = (π r² h) / 3

So, we have:

V = (π * 5² * 10) / 3 = 250 π / 3

So, how many times does Kim has to scoop (S):

`S = (4000 \pi /3 )/(250 \pi /3 ) = 16`

So, Kim will have to scoop 16 times with this second cup.