Question

1. Ki’von has a sink that is shaped like a half-sphere. The sink has a diameter of 20 inches. One day, his sink clogged. He has to use one of two different cups to scoop the water out of the sink. The sink is completely full when Ki’von begins scooping. (a) What is the exact volume of the sink? Show your work. (3 points) (b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points) (c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points)

Answer 1

Step 1
Find the volume of a sink
Volume sink=(4/6)*pi*r³ (half-sphere)
Diameter=20 in--------------> r=D/2-----------> r=10 in
Volume sink=(4/6)*pi*10³---------> (2000/3)*pi in³ --------> 2093.33 in³

(a) What is the exact volume of the sink? 
the answer part a) is (2000/3)*pi in³  (2093.33 in³)

(b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it?

volume of a conical cup=pi*r²*h/3
diameter=8 in--------------> r=4 in
h=6 in
volume of a conical cup=pi*4²*6/3-----------> 32*pi in³

if one cup---------------------> 32*pi in³
  X---------------------------> (2000/3)*pi in³
X=(2000/3)*pi/(32*pi)------------> 20.83----------> 21 cups

the answer part b) is 21 cups


(c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it?

volume of a cylindrical cup=pi*r²*h
diameter=4 in--------------> r=2 in
h=6 in
volume of a cylindrical cup=pi*2²*6-----------> 24*pi in³

if one cup---------------------> 24*pi in³
  X---------------------------> (2000/3)*pi in³
X=(2000/3)*pi/(24*pi)------------> 27.77----------> 28 cups

the answer part c) is 28 cups