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.
(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.
(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.
Volume of the sink The formula for a complete sphere is V = (4/3) pi r^3 1/2 a sphere is just one half that amount V = 1/2 (4/3) pi r^3 = (2/3) pi r^3 r = 20/2 = 10 a radius (r) is 1/2 d V = (2/3) 3.14 10^3 V = 2093 cubic inches.
First cone V = (1/3) pi r^2 h pi = 3.14 (always) r = d/2 = 8/2 = 4 in h = 6 in Volume = (1/3) * 3.14 * 4^2 * 6 Volume = 1/3 * 301.44 Volume = 100.8
The number of scoops needed is Scoops = volume of hemisphere / volume of cone scoops = 2093/100.8 Scoops = 20.6 Scoops should be rounded to 21
2nd Cone. You just need to substitute the numbers for the second scoop into what I have done above. The answer is 83.3 which you have to round to 84. He better stick with the first cone (or is it a she).
