Answer:
(answer 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.
I got the answer 62.5 and then rounded to 63 cups.
(Answer 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 of scoops to the nearest whole number.
I got 15.625 and rounded to 16 cups.
Step-by-step explanation:
i took the written test too
By taking the quotient between the volume of the sink and the volume for each cone, we will see that both of your answers are correct.
First, we know that the sink has a volume V = (2000/3)*pi in^3
A) First she uses a cone of a diameter of 4 in and a height of 8 in.
Remember that the volume of a cone of diameter D and height H is:
V = pi*(D/2)^2*H/3
Then this cone has a volume of:
V' = (pi/3)*(4in/2)^2*8in = (pi/3) 32 in^3
The number of scoops needed to completely remove the water out of the sink is given by the quotient between the two volumes, it is:
[tex]N = \frac{(pi/3)*2000 in^3}{(pi/3)*32 in^3} = 62.5[/tex]
Rounding it, we get 63, so she needs to scoop 63 times.
B) This time the diameter is 8 in and the height 8 in, so the volume of the cone is:
V'' = (pi/3)*(8in/2)^2*8in = (pi/3)*128 in^3
This time, she needs to scoop:
[tex]N = \frac{(pi/3)*2000 in^3}{(pi/3)*128 in^3} = 15.625[/tex]
Rounding to the next number we get 16, she needs to scoop 16 times.
So yes, both of your answers are correct.
If you want to learn more about volumes, you can read:
https://brainly.com/question/10171109
