Question

anthonys sink is shaped like a half-sphere, and it has a volume of 700 pi cubic inches. it is compltely full of water, and he has two different cylindrical cups he can use to scoop out. The blue cup has a diameter of 4 inches and a height of 8 inches in the green cup has a diameter of 8 inches and a height of 8 inches. How many cupfuls of water will it take for him to empty his sink using each cup? In your answer, give the number of cupfuls it will take to empty the sink using each cup, and then explain how you calculate it.

Answer 1

To answer this question the first step is to find the volume of each of the cylindrical cups.

The volume of a cylinder is given by the following equation:

`V=\pi r{}^2h`

Where V is the volume, r is the radius and h is the height.

Find the radius of each of the cups by dividing their diameters by 2:

`\begin{gathered} rb=(4)/(2)=2 \\ rg=(8)/(2)=4 \end{gathered}`

Calculate the volume of each of the cups using the given values:

`\begin{gathered} Vb=\pi rb^2hb \\ Vb=\pi(2)^2(8) \\ Vb=32\pi \\ Vg=\pi(4)^2(8) \\ Vg=128\pi \end{gathered}`

It means that the blue cup has a volume of 32pi cubic inches and the green cup has a volume of 128pi cubic inches.

To find how many cupfuls of water will it take for him to empty his sink using each cup, divide the volume of the sink by each of the volumes of the cups:

`\begin{gathered} nb=(700\pi)/(32\pi)=21.88 \\ ng=(700\pi)/(128\pi)=5.47 \end{gathered}`

It will take 21.88 (22) blue cups for him to empty the sink.

It will take 5.47 (6) green cups for him to empty the sink.