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Let's do this question, a conical Wesson is full of water, a spears dropped into the vessel such that

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it touches the sides and is just immersed in the radius of the clinical vessel is nine centimeter and

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height is 12 centimeter.

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What fraction of water spills out?

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All right.

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What's the video?

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Give it a try and then let's do it together.

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All right.

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We are back.

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Let's do it together.

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Now, over here we have a conical vessel and a spear is dropped.

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Right.

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And it's given that it touches it and it is just immersed.

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So this is how the spear is located.

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Now we need to find the fraction of water that spills out.

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Right.

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What does that mean?

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That would be the volume of the spear.

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Right.

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Divided by the volume of the cone, because the fraction of water that spills out will be equal to the

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volume of the spear.

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Right.

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And because we want to know what percentage fraction of water that spills out means, what percentage

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of the water that's already there in the cone is going out.

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So that's why we need to take the ratio volume of the spear divided by volume of the cone.

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All right.

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Well, let me draw a line over here.

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OK, now it's given that the radius is nine centimeter and the height is 12 centimeter to over here.

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If you take this part, you see you get it right angled triangle.

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Let me draw that over here.

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So this is nine centimeters.

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This is 12 centimeters.

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So Asper Pythagoras's theorem, this side will be root of 12 squared plus nine square.

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That's equal to 15.

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Right.

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So this side over here is 15.

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All right.

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Now, let me draw this part over here.

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All right, so I have nine over here and nine over here because the radius is given us nine.

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Right.

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And this spear is touching over here because it is just immersed and it touches the core.

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Right.

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So you have a point of contact over here and the point of contact here.

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Now, you can see that this and this has to be equal, right?

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Because when you look at it from this section, this is actually a tangent from an external point to

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a circle right there for this.

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And this has to be equal to this and this has to be equal.

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Let's make sure that this is nine centimeter and this is nine centimeter.

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All right.

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Now, over here, we know that this side over here, that is this much has to be 15 centimeters, therefore,

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because this part over here is nine.

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This part over here has to be 15 minus nine.

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That's equal to six centimeters.

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Right.

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And similarly, over here also you have six centimeters.

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Now, this circle over here is the inner circle of this triangle.

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Right?

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So let's mark that over here.

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This would be the in radius.

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All right.

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And remember, so because this is inscribed inside this triangle, these angles will be 90 degrees.

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Right.

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Or these.

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Sites are tangents, all right, now over here you have three areas are and we know that the high desert

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will there.

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Therefore this measurement will be 12 miners are right now.

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Let's take out this triangle over here where this site is.

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12 miners are.

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One are.

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And this site is six.

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Let's draw it over here.

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So you have a triangle over here where this site is 12 miners are.

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This is odd.

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And this is six right now.

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As per Pythagoras's theorem, 12 miners are square will be equal to our square plus six square.

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That's 36.

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So let's simplify this.

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We get one forty four plus square minus 24 hour is equal to our square plus 36 or on simplifying, you

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get twenty four hours equal to one zero eight.

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And that gives you are is equal to four point five.

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Right now we need to find the ratio of the volume of the spill to the volume of the cone.

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Right.

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But let me make some space over here.

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We know that the volume of the spear will be four by three by tube and the volume of the cone is one

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by three by a square inch.

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Right now, in these two cases, the radius is not the same.

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Right over here we are taking the radius of the spear and this is the radius of the cone.

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Now, let's substitute the values over here.

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And remember, we can cut out by and by and three and three right to all your radius of the spear is

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equal to four point five centimeter and radius of the cone we have about nine centimeter and height

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is equal to 12 centimeters.

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So let's substitute we get four into four point five.

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The whole cube divided by nine square into 12.

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Right.

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And this becomes nine by twenty four.

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And that is your answer, right.

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You can simplify it to three by eight.