A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the water rise in the barrel? I WILL GIVE BRAINLIEST!!! PLEASE HELP!!!
Answers
Answer:
Answer: 5/12 or approx. 0.42
Step-by-step explanation:
The ball will displace as much water as its volume.
Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.
Volume of a sphere:
[tex]V_s=\frac{4}{3} \pi r^3[/tex]
The radius is half the diameter. The diameter of the sphere is 10, thus:
[tex]r = d/2 = 10/2 = 5[/tex]
5^3 = 5*5*5 = 25*5 = 125
[tex]V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125[/tex]
The volume of a cylinder, which will be the shape of the increase in water, is the following:
[tex]V_c=\pi r^2 h[/tex]
We know the radius r, as we know the diameter.
[tex]r=d/2=40/2=20[/tex]
[tex]V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400[/tex]
We are looking for the height of the cylinder, h, as that will be the height of the water rise.
Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:
[tex]V_s = V_c[/tex]
[tex]\frac{4}{3} * 125 * \pi = 400 * h * \pi[/tex]
We can get rid of pi by dividing both sides by pi:
[tex]\frac{4}{3} * 125 = 400 * h[/tex]
And now divide both sides by 400:
[tex]\frac{4}{3} * \frac{125}{400}= h[/tex]
Just reversing it and putting h to the left:
[tex]h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}[/tex]
I see that I can divide both the numerator and the denominator by 4:
[tex]h =\frac{125}{3 * 100}= \frac{125}{300}[/tex]
I'll now divide both the numerator and the denominator by 25 to simplify the expression:
[tex]h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}[/tex]
Answer: The water rises by 5/12 (five twelfths).
If I want an approximate decimal answer, I can simply run this expression in a calculator:
[tex]\frac{5}{12}[/tex] ≈ [tex]0.416666667[/tex] ≈ [tex]0.42[/tex]
The amount of water rise is 0.42 and this can be determined by using the formula of the volume of the sphere and the cylinder.
Given :
A stone is dropped into a barrel of water and sinks to the bottom.
The ball is completely covered by water.
The following steps can be used in order to determine the water rise in the barrel:
Step 1 - The formula of the volume of a sphere is used in order to determine the water rise in the barrel.
Step 2 - The volume of a sphere is given below:
[tex]\rm V_s=\dfrac{4}{3}\times \pi \times r^3[/tex]
Step 3 - Substitute the values of the known terms in the above expression.
[tex]\rm V_s=\dfrac{4}{3}\times \pi \times \left(\dfrac{10}{2}\right)^3[/tex]
Step 4 - Simplify the above expression.
[tex]\rm V_s = \dfrac{4}{3}\times \pi \times 125[/tex] --- (1)
Step 5 - The volume of the cylinder is given below:
[tex]\rm V_c= \pi\times \left(\dfrac{40}{2}\right)^2\times h[/tex] --- (2)
Step 6 - Equate expression (1) and (2) in order to determine the value of 'h'.
[tex]\dfrac{4}{3}\times \pi \times 125= \pi \times 400 \times h[/tex]
Step 7 - Simplify the above expression.
[tex]\rm h = \dfrac{4\times 125}{3\times 400}[/tex]
h = 0.42
For more information, refer to the link given below:
https://brainly.com/question/16924154
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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hope this helps you ;)
pls give me brainlest :)
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2) Set up the problem showing the equations you’ll use. Please make sure you label or explain what your variables mean.
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Answers
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Answers
Answer:
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Step-by-step explanation:
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WILL GIVE BRAINLIEST!!!
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Step-by-step explanation:
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Answers
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Answers
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Answers
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Answers
Answer:
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Answers
Answer:
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I need to know the answer
