Respuesta :
Answer: The volume of the sink shaped like a half sphere is [2000/3] π in^2.
a) The volume of a cylinder is the area of the base * height
For this part the cup has a diameter, d, of 4 in and height, h, of 8 in.
The area of the base is π (d/2)^2 = π (2 in)^2 = 4π in^2.
The volume of the cuo is 4π in^2 * 8 in = 32π in^3.
Then the number of cups to take the volume of [2000 / 3] π in^2 is:
[2000 / 3]π / [32π] = 20.83
Answer: 21 cups.
b) For this part the diameter of the cup is 8 in and the height is 8 in
Then the volume is π (4 in)^2 * 8 in = 128 ⇅ in^3
And the number of cups needed is [2000π/3] / (128π) = 5.2
Answer: 5 cups
Step-by-step explanation:
The number of cups must Anthony scoop out of the sink with this cup to empty it in the first case is 10 and in the second case is 3.
What is Geometry?
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 1000 in³.
One day, his sink clogged.
He has to use one of two cylindrical cups to scoop the water out of the sink.
The sink is completely full when Anthony begins scooping.
(a) One cup has a diameter of 4 in, and a height of 8 in. The water of cup must Anthony scoop out of the sink with this cup to empty it will be.
[tex]\rm Number \ of \ cup = \dfrac{volume \ of \ half-sphere}{volume \ of \ cylinder} \\\\\\Number \ of \ cup = \dfrac{1000}{\frac{\pi}{4}d^2h}\\\\\\Number \ of \ cup = \dfrac{1000}{\frac{\pi}{4}*4^2*8}\\\\\\Number \ of \ cup = 9.947 \approx 10[/tex]
(b) One cup has a diameter of 8 in, and a height of 8 in. The water of cup must Anthony scoop out of the sink with this cup to empty it will be.
[tex]\rm Number \ of \ cup = \dfrac{volume \ of \ half-sphere}{volume \ of \ cylinder} \\\\\\Number \ of \ cup = \dfrac{1000}{\frac{\pi}{4}d^2h}\\\\\\Number \ of \ cup = \dfrac{1000}{\frac{\pi}{4}*8^2*8}\\\\\\Number \ of \ cup = 2.4867 \approx 3[/tex]
More about the geometry link is given below.
https://brainly.com/question/7558603
