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Video: Finding the Total Surface Area of a Cylinder given Its Height and Base Diameter

Kathryn Kingham

Find, to the nearest tenth, the total surface area of this cylinder.<Figure>


Video Transcript

Find to the nearest tenth the total surface area of this cylinder.

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. The net of a cylinder looks like this. And we need to find the area of the two circle bases and then the rectangle from the middle.

We first find the area of the circle and we multiply that by two because there’re two bases. And then we add the area of the rectangle. 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. And don’t forget to bring down your two because we have two circle pieces.

And we find the area of a rectangle by multiplying base times height. You recognize right away that the height of this rectangle is 12 millimetres, but the base is not as intuitive. The base of the rectangle, or maybe even you would call it the length of the rectangle, is the distance around the circle. The circumference, the distance around this circle, is the length of our rectangle. And what it is the formula for finding the circumference of a circle? It’s 𝜋 times the diameter.

Okay, now we have our full formula. Surface area of a cylinder looks like this: two times 𝜋𝑟 squared plus 𝜋 times the diameter times the height. Let’s start plugging in values. We’re given 16 millimetres, which is the diameter of the circle. But we need to know the radius; the radius is half of the diameter. The radius in this case would be eight millimetres. So we’ll plug in eight and then eight squared. We need the diameter to find the area of the rectangle portion, so we plug in 16 for the diameter.

And the height of our cylinder is 12. 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. But I remember that the question asked me to round to the nearest tenth, so I say 1005.3. And then I don’t forget my units, millimetres squared. The total surface area of this cylinder, 1005.3 millimetres squared.