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Question

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[-/3 Points] DETAILS MY NOTES (OU F5t2l Exz0t Prebel-02011} anane Circulz cone 0u netam6 and base radivs nas (olBI sunace arez Consisua ol IL base arez side area leadina the (crmulg: "7+hz suppore YcU *art Langent Iine approtimalion cone ofneighl Andcbdse [dn "Du ant change tne Dimensidns Eelnatc#c nX Ualue Lavaare Recancnal taceanc [DdWumacAre May Lal thetatal sUrtaze arEd reniains Mame suppdie increale the neighl DI Latcicm` VAE The estimared walue Orr Fcmcensuer



Answers

Find the lateral area and surface area of each right cone. Give your answers in terms of $\pi$
(GRAPH CANT COPY)

Here. We have a picture of the cone and we want to find a lot of oil in circus area of this cone. So my lateral area, the formula is pie. No. And l represents my slant height. Some my radius is 14th. So pi times 14 times 22 and this gets me three feet. Pi meters squared. So this is my latell area. To find my surface area, I need the area of the base which is a circle. So pi r squared high times. My art is 14 squared and I get 1 96 Hi. In squared at these two someone 96 pie plus 3 +08 high And I get a total of five for hi m squared as my total surface area.

All right, we've made it to the last question on this table. So once again, I'm gonna sketch the cone and find all the missing pieces to this table. So my cone do a general sketch of a cone. So this cone has a radius of nine. We do not know h or L, but we do know the volume and the volume is 3 24 pi. So we're gonna start by using a volume to help us find one of our missing variables either. H r l. So the formula for volume is 1/3 pie r squared h. So I'm gonna replace all the values that I know. So I know that the volume is 324 pi. So I'm gonna take out my V and put that in there of 1/3 pie. And my radius is nine squared each. So the only variable that I have that you need to solve for is R h. So nine squared is 81 81 divided by three is 27. So I'm gonna have 27 pi h on the right, and I have 3 24 pipe on the left. So since I'm solving for H. I must isolate that. So I'm gonna divide out 27 pi on both sides. The simplify. So one so H is equal to 12. So 3 24 divide where 27 is 12 in the price. Go to one. So that is one of my variables. So now that I have two of the three variables on a right triangle, I confined the 3rd 1 So I'm gonna do that. So let's pull out that right triangle from the cone. I know that my height is 12 Another my radio says nine. So I need my l. So using the Pythagorean theorem l is gonna be my C and 12 9 Grammy Met A M B. So 12 squared plus beast. Sorry. 12 squared plus nine squared equals l squared. Um, I can go through that process. Simplify. I'm gonna take the square root of all sides and l is going to give me 15. So now I have my last piece, which is my l. And that is 15. All right, so now I just need to find my lateral area, my total area. So let's start with the lateral lateral equals pi R L my radius is nine. And my, uh, slant height is 15. So my radius is nine of my slam highest fifteens arm replacing my arm. I l calculating that out nine times 15 as 135. So my lateral areas 135 hi units squared. And then, lastly is my total area, which is equal to pi r l plus pi r squared already no pyro because I just calculated it. That's the lateral area. So 135 pie plus pi times my radius squared, which is nine squared. So 135 pie plus 81 pie which equals 216 pie units squared and that completes my table.

We have phone number problem of 40 which is from the geometry and then later to corn. Okay, we need to find the letters of this area of this gun. We know that lateral surface area to see Elsa of corn equal to by R. L. L. Is there slant height? This is And so I think this particular so L could be found out using pythagorean identity. It is on that battle was not an entity 45 plus nine spiv. So this will give come 1600 plus 81. So this is 1681 The squad out. So this will become equal to 41 centimeters. The value of slant height is 41 centimeter. So lateral surface area will be able to buy into 41. This is L. An artist nine. So 369 5 will be the lateral surface area. So B is the correct answer. This is quite simple problem based on simple formula. Beat the corrections. Thank you so much. Have a nice day.

In this problem, we are given a cone which is being completely filled with ice cream. And this one makes a kind of human spirit kel scoop on top of it. So basically if you draw the diagram of the school with the hemispherical uh scoop, we will get a diagram like this. And the top radius is given a seven centimeter as well as the height of the corn is given as seven centimetres. So we have to find the complete volume of this uh of the school which has hemispherical scoop on top of it. So basically we have two different shapes over here. The bottom one is the coun And the top one is the hemisphere. So if you can find the volume of the school and added with the volume of the hemispheric hemisphere will get the complete volume of this ice cream court. So first let's find the volume of the corn. This is uh Equal to its right the form. No this is one x 3 by r squared hitch. And let's substitute the violence or here. So this is going to be on by 35 times three areas of the coal is seven centimetre. So we'll put sound square times height of the corn is seven. So basically this is uh Point Time seven Cube boy three seven cube is Equal and 2 3 43. So we can write down this as 343. Bye bye. Three centimeter cube sensitive volume. We put the universe and meter. Keep now we find the volume of the hemispherical shape will loom off. He means spear And we can install form. Now that is two x 3 by Cube. So let's substitute the radius over here. This is going to be five times It is is still seven. So this will be seven cube. So if you multiply and simplify this 3 43 Times two This is equal to 6 86. So we get 6 86 5 by three centimetre cuba. So these are the two volumes which we have obtained. So let's add them together and simplify so that we get there volume of the complete cone. So basically we have to add these two volumes. That is this one plus this one. So volume of coal. The complete cool or the ice cream corn is equal to 3 43 by by three. Press 6 86. Well I buy three so we can since we have the common denominator three we can add them as place it is three for three ply and six cities explain both are like them. So when we added we will get uh 343-686 just equal to 10-9 by three. As it is given in the question we can Use the Value of Fires 22 x seven. So that we can simplify this. This is 10-9 Times 22 x seven They went by three. So let's simplify this. You're to multiply by 22 With 10-9 and they went by 21. And when we do this, we will get 1078. So this is basically the only after the complete ice cream court that there's 1000 sound 78 centimeter cube, so that's the correct answer for this crime.


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