7 5 an observatory similar to the australian astronomical...

7) 5. An observatory, similar to the Australian Astronomical Observatory, has the shape of a right circular cylinder surmounted by a hemisphere and needs to be repainted. a. Determine the total area that will be painted. Round to the nearest tenth. 24 ft T 32 ft b. If one gallon of paint covers 300 ft², how many gallons are needed to paint the surface if it requires two coats? Gallons of Paint

Transcript

00:01 Okay, so i see that you need help with this question, and it says an observatory has the shape of a right circular cylinder topped by a hemisphere.

00:09 The radius of the cylinder is 8 feet.

00:13 The altitude is 26 feet.

00:20 What is the approximate surface area of the observatory? round to the nearest foot.

00:27 So it wants to know the surface area.

00:31 So to find the surface area of the observatory, you need to find the surface area of the cylinder, and that is just the lateral surface area.

00:47 So i'm going to use the formula of 2 times pi times the radius times the height plus 2 times pi times the radius squared, because it's only half of the sphere.

01:08 So i'm going to do 2 times pi times the radius of 8 times the height of 26 plus 2 times pi times the radius of 8 squared.

01:23 So 2, so i'm just going to multiply 2 times 8 times 26.

01:34 So that's 416 pi plus 2 times 8 times 8.

01:43 So that's 128 pi.

01:47 So that's 416 plus 128.

01:51 So that's 544 pi times 3 .14.

01:59 And so that's equal to 1 ,708 .16, and that is feet squared.

02:08 So then it says, so that's the surface area, okay? so then it says, remember, the top and the bottom of the cylinder will not be painted.

02:26 So then if the top isn't painted, then this is just the portion that's going to be painted.

02:39 So painted is going to be 416 times 3 .14.

02:47 So that is going to be 1 ,306 .24 feet squared is going to be painted.

02:55 And then it says, however, note that the hemisphere dome will be painted...

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