Find the lateral surface area of the following cylinder: 0=5cmcmLSA = [ ? Jn cm?Leave your answer in terms of T:Enter the number that goes in the green box:Enter...

Find the lateral area and surface area of each right cylinder. Give your answers in terms of $\pi$. a cylinder with base circumference $16 \pi$ yd and a height equal to 3 times the radius

Given a cylinder with the radius of 7.2 cm and a height of 13.4 cm, find the lateral surface area so the lateral surface area and they call it S. A. is equal to two pi R. H. So they gave us a radius of 7.20 cm And they gave us a height of 13.4 cm. So plugging in these values, solving for the surface area, and we get To three significant figures 606 square centimeters. So this is 36 figs. This is 36 figs. So your answer answer should be 366.

To find the lateral area and surface area of a cylinder. Let's go ahead and start with the formulas. The lateral area is going to be equal to two pi age are Where are Zehr? Radius ages the height? Um, and don't forget two Pi R is the circumference of this kind of like finding the perimeter, the circumference of the circle base and multiplying it by it tight. And then the surface area is equal to the lateral area, plus the area of both faces in the area of the base Pi r squared because it's a circle. Now let's make sure we know what we're given. We haven't our radius of three and a height of four, and that's pretty much everything we need in order to find each of these values the lateral area. But substitute what we know. Two pi and then h is for our is three were asked to keep the answer in terms of pie, so we're gonna keep Aya's itself and just simplify the product of 23 and four. So lateral area is equal to two times four is eight times three is 24 pi and our units are feats We're gonna have square feet. The surface area is equal to the lateral area that is 24 plus twice the area of each base area of the base. Being a circle area is going to be pi r squared, we know are so we can go ahead and substitute those values Pi times three squared or nine pie. So this is going to give us 24. Oh, I forgot my pie 24 pi plus 18 pie. And our final surface area is 24 plus 18 which is 42. Hi. And the units again, our feet 24 pi square fee.

Before we find the lateral area and surface area of the cylinder, let's write down the formulas we're going to need. The lateral area is going to be equal to two pi r H r is the radius h is the height and then the surface area is equal to the lateral area, plus the area of both faces and in this case, the area of the base. Each base is pi r squared because it's a circle were given a diameter of 15 yards and a height of 12 yards. So normally we would think, Hey, it's a diameter, the diameter is equal to two are And then maybe we would solve for R because that's what the formula calls for. But instead, let's remember that to our is the same thing as the diameter. So we can just plug in 15 instead of having to worry about finding our first. So doing that we have our lateral area is equal to two are which is our diameter substitute 15 times pi times the height The height is 12. This will simplify to 15 times 12 is 180 and then pie, with our units being yards so Our lateral area is 180 pie yards square. We're gonna substitute the 180 pie in for our lateral area in the surface area formula. We're gonna add to it twice for the area of the base. We know our because we can divide the diameter by two. So we kind of do needed at this 20.15 divided by two in our equal, 7.5. So we're gonna substitute the area formula. We've got pie, and then 7.5 squared. This will give us 180 pie plus 7.5 squared is 225 4th and trying to keep it exacts. I'm gonna go with fractions here. This value is going to come down to 225 4th times two. We're gonna put that pie out there and get pi and simplifying a little bit more. 180 pi plus, Let's see, we've got, um, 225 have spy, and then finally, we can conclude our surface area is equal to 180 plus 225 divided by two. If we keep it in exact form, that's 585 halves pie. And don't forget your units of yard squared and there you go

Let's find the lateral area and surface area of the cylinder to find the lateral area that is going to be equal to two pi h r. We're given our height is seven and R radius, but were given the diameter, so we're gonna have to take the diameter and divided by two are diameter is 11 which means the radius will be 11 house. Substituting these values in for our lateral area. We have two times pi times seven times 11 halves for a total of 77 high. The surface area is equal to the lateral area, plus twice the area of the base. The area of the base is equal to pi R squared, which is equal to 11 halves squared pie. We simplify that the area of the base is 121 fourth pie. We're going to substitute these values for our area of the base and the lateral area into the surface area. And we'll have 77 pi plus twice 1 21 divided by four pi. When we simplify 77 pi plus 1 21 halves keeping our answer exact. We need to have a common denominator. So I'm gonna write 77 pi as 154 halves pi plus 121 half spy for a surface area that is equal to 275. Have a pie and I almost forgot my units. Let's go ahead and add square inches to the lateral area. 77 pi square inches. In our surface area, 275 halves Score pi square inches.