Question

Carissa 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 Carissa begins scooping. Hint: you may need to find the volume for both. 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. 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 of scoops to the nearest whole number, and make certain to show your work. Answer:

Answer 1

1. Carissa must scoop out of the sink 125 cups of water with the first cup to empty it.

2. Carissa must scoop out of the sink 31 cups of water with the second cup to empty it.

Explanation:

1. Let's calculate the volume of the first cup, this way:

d = 4 ⇒ r =2

Volume of the first cup = π * r² * h /3

Volume of the first cup = π * 2² * 8 /3

Volume of the first cup = 32/3π in³

2. Let's calculate the volume of the second cup, this way:

d = 8 ⇒ r = 4

Volume of the second cup = π * r² * h /3

Volume of the second cup = π * 4² * 8 /3

Volume of the second cup = 128/3π in³

3. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the first cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the first cup

Number of cups = (4000π/3)/(32π/3)

Number of cups = 4,000π/3 * 3/32π (multiplying by the reciprocal)

We eliminated 3 and π in the numerator and denominator

Number of cups = 4,000/32 = 125

4. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the second cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the second cup

Number of cups = (4000π/3)/(128π/3)

Number of cups = 4,000π/3 * 3/128π (multiplying by the reciprocal)

Number of cups = 4,000/128 = 31.25

We eliminated 3 and π in the numerator and denominator

Number of cups = 31 (rounding to the next whole)