Answer:
<u>1. Carissa must scoop out of the sink 125 cups of water with the first cup to empty it.</u>
<u>2. Carissa must scoop out of the sink 31 cups of water with the second cup to empty it.</u>
Step-by-step 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
<u>Number of cups = 4,000/32 = 125 </u>
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
<u>Number of cups = 31 (rounding to the next whole)</u>