Question

Help me asap please! :D

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

Answer: See each part below:

a) The volume of a sphere is (4/3)pi(r^3). If you input a 10 for the radius of sink, you will get 4000/3(pi). However, we have to divide it by 2 since it is a half-sphere. So the volume is 2000/3(pi).

For each cone, the volume formula is: pi(r^2)h/3.

b) With a radius of 4 and a height of 6, the volume is 100.53. Dividing the volume of the sink by this takes 21 scoops.

c) With a radius of 2 and a height of 6, the volume is 100.53. Dividing the volume of the sink by this takes 84 scoops.

Answer 2

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