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Carissa also has a sink that is shaped like a half sphere. The sink has a volume of 4000/ 3 * π in 3. One day, her sink clogged. She has to use one of the two CONICAL cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping. Hint: you may need to find the volume for both.

A: one cup has a diameter of 4 in. and a height of 8 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, and make certain to show your work.

B: One cup has a diameter of 8 in and a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number to the nearest whole number and make certain to show your work.

Please make sure you are correct before attempting to answer it.
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Respuesta :

calculista

Answer:

Part a) 119 cups

Part b) 30 cups

Step-by-step explanation:

Part a)

step 1

Find the volume of the conical cup with a diameter of 4 in. and a height of 8 in

The volume of the cone (cup) is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=4/2=2\ in[/tex] ----> the radius is half the diameter

[tex]h=8\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(2^{2})8=33.49\ in^3[/tex]

step 2

Find out how many cups of water must Carissa scoop out of the sink

Divide the volume of the sink by the volume of the cup

so

[tex]\frac{4,000}{33.49}= 119\ cups[/tex]

Part b)

step 1

Find the volume of the conical cup with a diameter of 8 in. and a height of 8 in

The volume of the cone (cup) is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=8/2=4\ in[/tex] ----> the radius is half the diameter

[tex]h=8\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(4^{2})8=133.97\ in^3[/tex]

step 2

Find out how many cups of water must Carissa scoop out of the sink

Divide the volume of the sink by the volume of the cup

so

[tex]\frac{4,000}{133.97}= 30\ cups[/tex]