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Determine to the nearest 10th the lateral surface area of the cylinder shown.
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The lateral surface area will be the surface area of this cylinder except for the bases.
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So we will be excluding the circles.
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So if we think about the cylinder, we can imagine this as a soup can.
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And the lateral surface area would be the soup can label, again excluding the lid and the bottom.
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So if we would imagine peeling off the label from the soup can, and this label is a rectangle, length times width, that is our lateral surface area formula for the cylinder.
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And this is because, again, itβs a rectangle.
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Now in the rectangle, the width is here.
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But in the cylinder, the width we would consider the height.
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And the length, this distance, it would be the distance that wraps around the lid.
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And the distance around a circle is circumference.
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And the circumference of a circle is two times π times the radius of the circle.
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So in our formula, we can replace πΏ with two times π times the radius and the width with the height.
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So the height we know is 23 feet.
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Now the radius is the distance from the centre of a circle to a point on the circle, which would be here.
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And it tells us that distance is 13 feet.
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So two times 13 is 26.
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So 26π feet times 23 feet would be equal to 598π feet squared.
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Now we need to multiply by π.
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And we get approximately 1878.67 feet squared.
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But we need to round to the nearest 10th.
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So we need to round where the six is.
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So we will either keep the six a six or round it up to a seven.
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So looking to the number to the right, the seven that is larger or equal to five, that means we will round six up to seven.
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Therefore, the lateral surface area of this cylinder shown would be 1878.7 feet squared.