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Find to the nearest tenth the total surface area of this cylinder.
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Finding the surface area of a cylinder looks like this: finding the area of the base, multiplying that by two, and then finding the area of the rectangle that’s formed between the two bases.
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The net of a cylinder looks like this.
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And we need to find the area of the two circle bases and then the rectangle from the middle.
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We first find the area of the circle and we multiply that by two because there’re two bases.
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And then we add the area of the rectangle.
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To find the area of the bases, which are circles, we use the formula for finding area of a circle, which is 𝜋 times the radius squared.
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And don’t forget to bring down your two because we have two circle pieces.
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And we find the area of a rectangle by multiplying base times height.
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You recognize right away that the height of this rectangle is 12 millimetres, but the base is not as intuitive.
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The base of the rectangle, or maybe even you would call it the length of the rectangle, is the distance around the circle.
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The circumference, the distance around this circle, is the length of our rectangle.
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And what it is the formula for finding the circumference of a circle?
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It’s 𝜋 times the diameter.
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Okay, now we have our full formula.
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Surface area of a cylinder looks like this: two times 𝜋𝑟 squared plus 𝜋 times the diameter times the height.
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Let’s start plugging in values.
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We’re given 16 millimetres, which is the diameter of the circle.
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But we need to know the radius; the radius is half of the diameter.
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The radius in this case would be eight millimetres.
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So we’ll plug in eight and then eight squared.
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We need the diameter to find the area of the rectangle portion, so we plug in 16 for the diameter.
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And the height of our cylinder is 12.
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The area of our circle base times two equals 402.12, the area of the rectangle portion 603.19, when I add those together, I get one 1005.31.
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But I remember that the question asked me to round to the nearest tenth, so I say 1005.3.
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And then I don’t forget my units, millimetres squared.
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The total surface area of this cylinder, 1005.3 millimetres squared.