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tyrasimpson4787
07.08.2019 •
Mathematics
Acone shaped paper water cup has a height of 12 cm and a radius of 6 cm. if the cup is filled with water to half its height, what portion of the volume of the cup is filled with water?
exactly of the cup is filled with water.
(type a simplified fraction)
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Ответ:
The portion of the volume of the cup that is filled with water is![\frac{1}{8}](/tpl/images/0172/8945/7440a.png)
Step-by-step explanation:
step 1
Find the volume of the paper water cup
The volume of the cone is equal to
we have
substitute
step 2
If the cup is filled with water to half its height, find out what portion of the volume of the cup is filled with water
Remember that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
In this problem the similar cone has half the height of the complete cone
so
The scale factor is equal to 1/2
therefore
The volume of the cup that is filled with water is equal to the volume of the complete cup by the scale factor elevated to the cube
therefore
The portion of the volume of the cup that is filled with water is
Ответ:
Exactly _
__ of the cup is filled with water.
Step-by-step explanation:
The formula to calculate the volume of a cone is:
Where
r is de radius
h is the height
So the volume of the cone is:
The angle z that is opposite the radius of the cone is:
The amount of water that fills half the cone occupies the volume of a cone with radius R, height
and angle z = 26.565°
Therefore we have that:
and
Then portion of the volume of the cup is filled with water is:
Ответ:
0 but if u really think about it, it would still be 0
Step-by-step explanation: