To empty the sink 16 cups it will take for the blue one and 4 cups it will take for the green cup.
It is given that Anthony's sink is shaped like a half-sphere, and it has a volume of 512π cubic inches.
It is required to find how many cupfuls of water to empty the sink.
What is volume?
It is defined as a three-dimensional space enclosed by an object or thing.
We have:
Sink volume V = 512π cubic inches
The blue cup diameter d(b) = 4 in or radius r(b) = 2 in
and height h(b) = 8 in
The green cup diameter d(g) = 8 in or radius r(g) = 4 in
and height h(g) = 8 in
The cup is the shape of a cylinder we know the volume of a cylinder is given by:
[tex]V = \pi r^2 h[/tex]
Volume for the blue cup:
[tex]\rm v(b) = \pi\times 2^2 \times 8[/tex] [ r(b) = 2 in and h(b) = 8 in]
v(b) = 32π cubic inches
Volume for the green cup:
[tex]\rm v(g) = \pi\times 4^2 \times 8[/tex] [r(g) = 4 in and h(g) = 8 in]
v(g) = 128π cubic inches
For a number of blue cups:
[tex]=\frac{512\pi}{32\pi}[/tex] ⇒ 16
For a number of green cups:
[tex]=\frac{512\pi}{128\pi}[/tex] ⇒ 4
Thus, to empty the sink 16 cups it will take for the blue one and 4 cups it will take for the green cup.
Learn more about the volume here:
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