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