Question

HELP ME OUT PLS AND HAVE A SHORT ANSWER PLS!!!!!!!

Anthony's sink is shaped like a half-sphere, and it has a volume of 5121 cubic inches. It is completely full of water, and he has two different cylindrical cups he can use to scoop it out. The blue cup has a diameter of 4 in. and a height of 8 in., and the green cup has a diameter of 8 in. and a height of 8 in.. How many cupfuls of water will it take for him to empty his sink using each cup? In your answer, give the number of cupfuls it will take to empty the sink using each cup, and then explain how you calculated it. (NOTE: Type out your work & write out your explanation for full credit.)​

Answer 1

By taking the quotient between the volumes, we conclude that he must use the blue cup 16 times or the green cup 4 times.

How many times does he need to use each cup?

The volume of the sink is 512π in^3.

The blue cup is a cylinder of diameter = 4 in and a height = of 8 in, then its volume is:

V = π*(4in/2)^2*8in = 32π in^3

The number of times that he needs to use this cup is given by:

N = (512π in^3)/(32π in^3) = 512/32 = 16

He needs to use 16 times the blue cup.

The green cup has a diameter =of 8in and a height = of 8in, then its volume is:

V' =π*(8in/2)^2*8in = 128π in^3

The number of times that he must use this cup is:

N' = (512π in^3/ 128π in^3) = 512/128 = 4

He needs to use 4 times the green cup.

hope it helps

have a good day :)