Volume of Water Inside a Cup
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I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
asked Nov 22 at 11:22
user618548
1
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up vote
0
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favorite
I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
asked Nov 22 at 11:22
user618548
1
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 at 11:27
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
asked Nov 22 at 11:22
user618548
1
I came across this problem in School. Suppose I have a cup and suppose that the cup is cylinder. I know the total volume of the cup and I fill with some water.
Let $V_c$ be the volume of the cup, $V_w$ the volume of water and $h$ be the distance from the water to the bottom of the cup. I'd like to calculate the total volume of water inside the cup (the cup is not filled).
Here's what I thought: since the volume is proportional to the height I could do a basic cross multiplication, am I correct? Is there a way to write that result using integral?
integration volume
integration volume
asked Nov 22 at 11:22
user618548
1
asked Nov 22 at 11:22
user618548
1
asked Nov 22 at 11:22
user618548
1
asked Nov 22 at 11:22
user618548
1
asked Nov 22 at 11:22
user618548
1
1
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 at 11:27
add a comment |
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 at 11:27
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 at 11:27
Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 at 11:27
add a comment |
1 Answer
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You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 at 11:27
TonyK
41.2k352131
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up vote
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down vote
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 at 11:27
TonyK
41.2k352131
add a comment |
up vote
0
down vote
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 at 11:27
TonyK
41.2k352131
add a comment |
up vote
0
down vote
up vote
0
down vote
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 at 11:27
TonyK
41.2k352131
You need to know the height of the cup $-$ call it $H$. Then the answer is simply $V_w=dfrac{h}{H}V_c$.
You don't need to use integration here, because the shape of the cup is so simple. If it had a more complicated shape, you might need calculus.
answered Nov 22 at 11:27
TonyK
41.2k352131
answered Nov 22 at 11:27
TonyK
41.2k352131
answered Nov 22 at 11:27
TonyK
41.2k352131
answered Nov 22 at 11:27
TonyK
41.2k352131
41.2k352131
add a comment |
add a comment |
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Volume = Height x cross sectional area. So for circular cylinder $V= pi r^2 h$.
– user121049
Nov 22 at 11:27
If you want to use the integral, you're essentially integrating over the height of the cup, and the integrand is just the cross section (circle?) which is a constant.
– Matti P.
Nov 22 at 11:27