1. Jose has a sink that is shaped like a half-sphere. The sink has a volume of 1072 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 2 in. and a height of 4 in. How many cups of water must Jose scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
Answers
Answer:
Volume of a cup
The shape of the cup is a cylinder. The volume of a cylinder is:
\text{Volume of a cylinder}=\pi \times (radius)^2\times heightVolume of a cylinder=π×(radius)
2
×height
The diameter fo the cup is half the diameter: 2in/2 = 1in.
Substitute radius = 1 in, and height = 4 in in the formula for the volume of a cylinder:
\text{Volume of the cup}=\pi \times (1in)^2\times 4in\approx 12.57in^3Volume of the cup=π×(1in)
2
×4in≈12.57in
3
2. Volume of the sink:
The volume of the sink is 1072in³ (note the units is in³ and not in).
3. Divide the volume of the sink by the volume of the cup.
This gives the number of cups that contain a volume equal to the volume of the sink:
\dfrac{1072in^3}{12.57in^3}=85.3cups\approx 85cups
12.57in
3
1072in
3
=85.3cups≈85cups
Given : Jose has a sink that is shaped like a half-sphere. The sink has a volume of 1072 in³
cup has a diameter of 2 in. and a height of 4 in.
To Find : How many cups of water must Jose scoop out of the sink with this cup to empty it
Solution:
Volume of cup = πR²H
R = Radius = Diameter/2 = 2/2 = 1 inch
π = 22/7
H = height = 4 inch
Volume of cup = (22/7)(1)²4
= 88/7 inch²
Volume of sink = 1072 in³
Number of scoops = 1072 /(88/7)
= 1072 * 7 / 88
= 85.27
as there will be some water left after 85 scoops
Hence 86 scoops required
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