Sri Basara leads School basic IIT MATHS Class day-12

Ajouté : 2026-05-12

[00:00:02]So what is the volume of the hemisphere formula?

[00:00:19]TSA of hemisphere.

[00:00:24]>> Now write down the question once.

[00:00:28]Find the PSA of hemisphere with radius 14 cm.

[00:00:43]with the radius 14 cm.

[00:01:04]>> Tell me >> what is the formula of ta 3?

[00:01:11]B SA = V² 3 into 7 into 14 into 14. Yes. 7 2 Okay. 3 into 22 into 2 into 14.

[00:01:33]66 into 28. 66 into 284 184 8 cm square about is heavy sperical is heavy sperical with radius 3.5 cm. cm with radius 3.5 cm.

[00:02:12]Find its capacity.

[00:02:16]Find this capacity.

[00:02:22]So what they asking capacity means >> volume. Very good. So what is the volume of the hemisphere 2x3?

[00:02:34]Yes or no? What is the radius is given?

[00:02:36]>> 3.5 3.5 cm.

[00:02:41]So this is about half of the volume you are going to find. Yes or no? So tell me 2x3 into 2x into 3.5 into 3.5.

[00:03:03]Okay. Now 44 into 0.5 into 3.5= 3 by 10 into 35 10 52 and 5 77 into 3.5 is nothing but 77 cm >> 2 by 3 is there >> three by three there I multip >> 22 enough 77 by 3 cm cube.

[00:04:06]Find the CCA of the scale sphere of radius 7 cm of radius 7 cm of radius 7 cm.

[00:04:30]Tell me >> what is the radius is given 7 cm 7 cm.

[00:04:42]What is the CSA 2 r²?

[00:04:51]So 2 into 22 by 7 into 7 into 78 38 38 cm square 38 cm square.

[00:05:11]So for the area what is the units here?

[00:05:17]>> Uh unit square.

[00:05:20]Yes or no? Means how it will come square and so on. Then what about the global surface area and the lateral surface area?

[00:05:36]square. So same like normal surface area and lateral surface area and surface area also we use the what cime square or me square or m square. Then what about the volume?

[00:05:55]>> Yes the volume is nothing but unit cube or we can also say as cubic units. Okay.

[00:06:05]Now, so what is here? CMIM cube, me cube and kilome cube.

[00:06:14]Okay, now clear no doubt right.

[00:06:19]Next we're heading on right now write this also in second class we'll discuss the triangle and its properties.

[00:06:39]Yes or no in the chapter we'll discuss the uh centroid.

[00:06:45]Okay. Now you don't know. Next we don't know. Okay. Now centr and midpoint.

[00:06:53]Okay. Now we are going to find this. No.

[00:06:56]Yes or no? So how we are going to find this? By taking the two points and the first point is going as X and second point is going as Y. Okay.

[00:07:08]So distance between those two points if you want to calculate means then we are going to say as what is it midpoint or centroid or whatever it is we use. Okay.

[00:07:19]Now that process is known as a finite geometry.

[00:07:23]Okay. Now clear finding the distance or a midpoint or a cent or slope or or so suppose this is the line you're having.

[00:07:40]Okay. Now this is the line you're having.

[00:07:44]Okay. So what is here?

[00:07:48]What is this? It's not center. It's origin.

[00:07:54]Okay. Now so here to here this is comes as x >> xaxis.

[00:07:58]>> So here to here all the positive values we are taking all the positive values.

[00:08:05]Okay. Now here x dash it's nothing but all the negative values you're going to take.

[00:08:11]Okay. Now so from all z here at the yaxis. So here all you get the positive >> positive values. Okay. Now here what it is here to here you're going to have the negative values.

[00:08:31]>> Okay. Now for suppose here what point is there for suppose 1 comma 2 here from the origin can you take 1 2.

[00:08:43]>> No the origin always lies 0 because here it is starting. No. Yes or no? Zero after all positives. Zero before all negative.

[00:08:59]So here 0 comma 0 this is nothing but the x and this is nothing but the y.

[00:09:05]Okay. Now clear. So here 0 1 2 I have taken the point. It's nothing but this one belongs to x-axis and this two belongs to y ais.

[00:09:21]Okay. Now understand here means 1 2 means how we going to measure here one is there 2 3 here 1 2 3. So 1 comma 2 right? So here you have to 1 comma 2.

[00:09:41]Okay. Now understand here. So now we have to find the distance from here to here. What is the distance?

[00:09:51]from the point also to what 1 2 I want the distance to find the distance that is nothing but that formulas all using the coordinates of ring you understand this again say here what is the point 0 it's nothing but the origin okay now here all you get the positive values here also the positive values here also x negative neative values we have negative values okay now now we have taken the point 1 2 okay now or otherwise or otherwise I have taken the -1 -3 I have taken where is the minus1 here this side it is the minus one where is the minus3 here this is all the positive values no so here the negative values 1 2 3 so here 1 - 3 Now I want the distance between from the origin to point -1 - 3. Now you have to find the distance of this clear understand now the distance between the two points and the distance between the horizontal to any point I'll give you the formula right now keeping coordinate geometry coordinate geometry the distance from the distance from origin.

[00:11:34]So 0 comma 0 right this value never going to change. Okay.

[00:11:41]Now origin is zero. That's it. It's not positive. It's nothing. Okay. Now the distance from origin to point any point I'm taking x y.

[00:12:01]Okay. Now the first value always be the x value only. The second value always be the y value. It may have positive or negative.

[00:12:14]Okay. Now what is the formula?

[00:12:21]Is 2 / x² + y² x² + y square.

[00:12:39]The second one, the distance from the distance from the distance from two points.

[00:12:52]The distance from two points that is x1, y1 to x2, y2.

[00:13:04]These are the two points.

[00:13:07]Means here I have got this is a one point and here one point. Now I want to give these two.

[00:13:14]Okay. Now understand uh what is the formula? x1 x2 - x1² + x2 - x1² + y - y1 square. Very good.

[00:13:38]is the midpoint of the midpoint of X1A Y1 X2A Y2 in the sub.

[00:14:10]We want the big point. Now I told we are taking the two points distance. Okay.

[00:14:16]Now this is the distance between the two points. So then what is the formula we use? We use this formula. Now I want these two points about tell me x1 x1 + x2 by 2 y.

[00:14:32]>> So it is point is px y that is the midpoint.

[00:14:38]Now tell me x y = x2 y1 + y2 y1 + y2 by 2 Midpoint I already told you while explaining in the average is nothing but the mid value I told yes or no so here how many will be there two points no so that's taking the two okay now next a point if a point if a Point PX Y is dividing a line AB is dividing a line AB is dividing a line AB in ratio in ratio M1 is to M_sub_2 in ratio Show M1 S3 M2 where where a value is nothing but X1A Y1. B value is nothing but X2 Y2.

[00:16:12]Then a = x1 y1 comma b = x2 y.

[00:16:25]So this formula gave you in the ratio.

[00:16:28]What is that formula?

[00:16:32]>> What?

[00:16:37]Don't don't go that much. Just here I will not read anything.

[00:16:57]This formula I told on the ratios. Tell me that formula first formula m in the ratio. Yes or no? What is the formula?

[00:17:25]Say m + n is 2 or n by m + n.

[00:17:40]They gave you the ratio.

[00:17:42]If the ratio is not the exact value, if you want to find the exact number, just we use this for the s in the same way.

[00:17:50]This is also what is the ratio I give mist what are the points I give this first point and this is second point now tell me >> m1 m2 x1 m1 x2 + m1 x2 >> m2 x1 m2 >> m1 + m2 Comma comma comma 1 by Y2 + M1 Y2 + 2 Y2 Y1 by M2 Y12 but here suppose MG means we will write Okay. Now if a is a x1 y1 b x2 y2 c x3a y3 forms a triangle forms a triangle.

[00:19:26]If you want to construct a triangle, we need the three sides though that three sides measure this.

[00:19:36]Okay.

[00:19:40]The area of Then the area of a triangle is Then the area of a triangle is What is the area formula?

[00:20:20]>> Okay. Now, so half >> first X1 Y2 - Y3.

[00:20:32]Next which point >> x² >> y3us y3 - y1 >> y3 - y1 >> + x3 y1 + y2 y1 - y2 >> y1 - y2 clear right centroid.

[00:21:05]The cent of a triangle The center of a triangle A B C is What is the center of a triangle ABC?

[00:21:24]that point I want.

[00:21:29]P X Y is nothing but a point.

[00:21:32]Tell me X1 + X2 + X3 X3 Y3 Y1 + Y + Y3 Y3. So this is the cent point.

[00:21:53]Find the distance between Find the distance between Find the points.

[00:22:09]Find the distance between the points.

[00:22:15]- 2, 4 3 - 2.

[00:22:28]Tell me what is the distance?

[00:22:37]X2 - X1 + Y 2 - Y1² roo<unk> okay now. So now tell me what is X and what is the Y know this is X.

[00:22:57]Okay. Now tell me what is >> 3 + 2 3 + 2 + 2 - >> So + 2² + 2 means - 2 - 4.

[00:23:16]Okay. Now - 5² - 6 >> - 6² >> 256 >> 361 is the distance.

[00:23:49]Find the distance from origin.

[00:23:55]This is go 0 from all to 5a 12.

[00:24:15]What is the distance?

[00:24:24]>> 12.

[00:24:26]>> What is the formula?

[00:24:31]>> Y you can take it. So sorry 12 square + >> I square + >> roo<unk> of i square + 1 square + i² roo<unk> over so 144 + 25 >> 169 169 >> madam so 13 square and all get cancel so the answer is I will.

[00:25:25]Determine the distance between Determine the distance between.

[00:25:34]Then the distance between - 7A 8 and 1 - 2. Determine the distance between - 7A 8 and 1 -2. Tell me fast.

[00:25:57]What is the form that distance is equals to this is x2 y2 x1 y1. What is x2? 1 - 7 square + - 2 - 8 sorry - 8 square.

[00:26:22]Tell me into sorryUS 7 8² + - 10 - 8 - 10 square.

[00:26:40]So tell me 64us square >> 164 take any square 169 41.

[00:27:14]>> 221 241.

[00:27:28]Find the midpoint of Find the midpoint of -4A 5 and 8 - 3 - 4.

[00:27:43]Find the midpoint of -4A 5 and 8. What is the point for y1 + y2?

[00:27:58]X1 is X2 by 2. So what is X1 here? - 4 + 8 by 2 4.

[00:28:06]>> Okay. Now 5 + - 3 by 2 >> 2 by 2.

[00:28:14]>> So how much is this? 4 by 2 - 3 2 by 2.

[00:28:21]So comma is the midpoint.

[00:28:28]If the midpoint of if the midpoints of if the midpoint of points xa 4 6a 8 is 5a 6.

[00:28:53]If the midpoints of If the midpoint of points xa 4 6a 8 is the midpoint value is given you have to find the x point >> y= x= >> so what is the point x1 >> x1 + 5 6 Tell me x1 + x2 by 2 x + x2 x 6 by 2 uh >> 4 + 8 by 2 >> 4 + 8 by 2 >> 8 by 2.

[00:29:35]This is the x point. This is the x point. This is a y point and this is a y point. Then x values and y get equal.

[00:29:45]Procedure x + 6 by 2, 4 + 8 12 by 26.

[00:29:55]>> So 66 is equal then x is also equal.

[00:30:01]So what you going to take here?

[00:30:05]>> 5 = x + 6 by 2 when you go inside 10 = x + 6. So 10 - 6 = >> x = 4= x= find the coordinates of the point.

[00:30:34]Find the coordinates of the point dividing 1 7 n dividing 1 7 1 7 Find the coordinates of the point point dividing 1 7 9 3 in ratio 4 is to 5 in ratio 4 is to 5.

[00:31:20]So what is the coordinate point here?

[00:31:24]What is the formula? M1 X2 + X1 by M1 + M2 M1 M1 X2 + M2 >> X1 by >> X1 >> X1 by >> M1 + X1 + M2 m1 X2 + >> M1 Y2 + M2 Y1 + M2 Tell you what is the m1 value here four m2 value >> five.

[00:32:03]>> So 4 into x2 value >> 9 >> 4 into >> 9 >> x2 value what is x2 value?

[00:32:11]>> 9 plus what is m2 value.

[00:32:18]What is the x1?

[00:32:20]>> 1 5 what is the m1 x1? 9.

[00:32:25]>> Next, what is the value?

[00:32:33]>> 4 into what you're asking again?

[00:32:37]by 2 3 + 5 into 7 >> 4 + 5 >> 4 + 5 >> 36 + 5 >> 4 9 5 1 sir 5 >> 36 + 5 >> 40 by 9 >> 12 4 3 12 5 7 >> 3 >> 12 + 35 >> 47 >> 47 I >> So any cancer, >> right?

[00:33:19]So look at here.

[00:33:21]>> Find a point that divides the ratio.

[00:33:26]Find a point that divides the segment.

[00:33:30]- 2a - 2a -4 6a 8 and 6a 8 internally in the ratio 1 is to 1 in the ratio 1 is to 1. Now tell me this is the x1 y1 x2 y2. So tell me the formula what is it?

[00:34:00]point x y m1 means 1 into y2 sorry x2 >> x2 is what 6 plus again 1 into 1 - >> 2 - 2 y >> 1 + 1 into 1 into 8 + >> + 1 - 4 5 1 + >> 6 1 into - 2 - 2 - 6 - 2 >> 4 by 2 1 into 8 1 into - 4 - 4 8 - 4 by 2.

[00:34:52]So 2a 2 is the sorry so 2a 2 is the point it's point >> which divides which divides in find the area of a triangle.

[00:35:09]Find the area of a triangle with vertices with vertices.

[00:35:20]Find the egg of the triangle as 7a 2a 2 3a 8 - 1a 4.

[00:35:34]So what is the area formula? Half b into h. So here what is the formula?

[00:35:42]So this is x1 comma y1 x2 comma y2 x3 comma y3.

[00:35:52]So what is the area formula?

[00:35:55]Half >> x1 into y2 + y3 it >> so 8 - >> 4 plus >> next >> x2 3.

[00:36:27]4 - 2 >> 2 >> + again >> 3 - 1 into >> y1 - y >> y1 - y2 y3 - y1 2 - 2 >> y3 - y1 y - y3 >> y1 - y2 - y2 >> y1 - y2 2 2 - 8.

[00:37:01]So 1 by 2 7 into 8 - 4 4 + 3 4 - 2 2 - 2 - 8 - 6.

[00:37:15]>> Okay. enough. So now tell me 1 by 2 7 4 >> 28 + 6 6 + 6 >> 48 >> 40.

[00:37:26]>> So 28 + >> 40 40 >> 40 20.

[00:37:35]So the answer is 20. Area is nothing but any units.

[00:37:45]That's where you need to help me.

[00:37:59]Next, start from here.

[00:38:08]Find the cent of a triangle.

[00:38:11]Find the c of a triangle with vertices.

[00:38:18]Find the c of a triangle with vertices 1a 2 4a 5 7a 8.

[00:38:30]to find the cent of a triangle with the vertices 1A 2 4a 5 7 8. So what you going to do here?

[00:38:43]Formula simp x1 + x2 + x3 means 1 + 2 + 7 by 3 >> 1 + 4 + 7 1 + 4 + 7 by 2 + 5 2 + 5 + 8 >> 5 + 8 by 3.

[00:39:15]1 + 4 5 + 7 by 3 7 15 by 15 by 3 4a 5 is the cent point.

[00:39:39]>> So what we have discussed today applications on and then we discuss the points on the with the formulas we have discussed with the applications.

[00:39:56]>> Okay. Now what is today's question >> for applications prepare well. Thank you.

[00:40:04]>> Thank you ma'am.