The lateral surface area of a cylinder can be found using the formula:
Lateral surface area = height x circumference of base
Since the figure is not shown to scale, we cannot directly measure the height of the cylinder. However, we can use the Pythagorean theorem to find it.
The radius of the top circle is given as 18 in, so the diameter is 2 x 18 = 36 in. The circumference of the circle is πd = π x 36 = 113.1 in (rounded to one decimal place).
The height of the cylinder can be found by using the Pythagorean theorem with the given dimensions. We have a right triangle with the hypotenuse being the slanted side of the cylinder, which has length 15 in. One leg of the triangle is the radius of the top circle, which is 18 in. The other leg is the height of the cylinder (h).
Using the Pythagorean theorem:
18^2 + h^2 = 15^2
Simplifying:
324 + h^2 = 225
Subtracting 324 from both sides:
h^2 = -99
Since we cannot have a negative height, we know that there is no solution to this equation. This means that the cylinder cannot exist with the given dimensions.
Therefore, we cannot find the lateral surface area of the cylinder to the nearest whole number.
Find the lateral surface area of a cylinder to the nearest whole number the figure is not shown to scale
18 in the top circle. 1/2
15 in on the side
1 answer