Question

Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 4500/3 πin3. One day, his sink clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely full when Anthony begins scooping. One cup has a diameter of 6 in. And a height of 14 in. How many cups of water must Anthony scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. One cup has a diameter of 10 in. And a height of 12 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

`Scoops = 12` --- cup 1

`Scoops = 5` --- cup 2

Explanation:

Given

Hemisphere

`Volume = (4500\pi)/(3)\ in^3`

Cup 1

`Height = 14\ in`

`Diameter = 6\ in`

Cup 2

`Height = 12\ in`

`Diameter = 10\ in`

Required: How many scoop of each?

For cup 1

Calculate the volume

`Volume = \pi r^2h`

Where

`h = 14`

`r = (1)/(2) * 6 = 3`

`Volume = \pi r^2h`

`Volume = \pi * 3^2 * 14`

`Volume = \pi * 126`

`Volume = 126\pi`

Divide the volume of the hemisphere by the calculated volume of cup 1

`Scoops = (4500\pi)/(3) / 126\pi`

`Scoops = (4500\pi)/(3) * (1)/(126\pi)`

`Scoops = (1500\pi)/(1) * (1)/(126\pi)`

`Scoops = (1500\pi)/(126\pi)`

`Scoops = 12` --- approximated

For cup 2

Calculate the volume

`Volume = \pi r^2h`

Where

`h =12`

`r = (1)/(2) * 10 = 5`

`Volume = \pi r^2h`

`Volume = \pi * 5^2 * 12`

`Volume = \pi * 300`

`Volume = 300\pi`

Divide the volume of the hemisphere by the calculated volume of cup 2

`Scoops = (4500\pi)/(3) / 300\pi`

`Scoops = (4500\pi)/(3) * (1)/(300\pi)`

`Scoops = (1500\pi)/(1) * (1)/(300\pi)`

`Scoops = (1500\pi)/(300\pi)`

`Scoops = 5`