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)
Step 1 Find the volume of <span>a sink Volume sink=(4/6)*pi*r</span>³ (<span>half-sphere) Diameter=20 in--------------> r=D/2-----------> r=10 in </span>Volume sink=(4/6)*pi*10³---------> (2000/3)*pi in³ --------> 2093.33 in³
<span>(a) What is the exact volume of the sink? the answer part a) is </span>(2000/3)*pi in³ (2093.33 in³)
<span>(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?
</span>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
Probability of a tail for any on coin = 1/2 As the tosses of the 4 coins are independent of each other we multyiply the probs:- P(4 tails) = 1/2 * 1/2*1/2*1/2 = 1/16
