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
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.
To find the lateral surface area of a cylinder, we need the height and the radius. However, with the given information, we only have the radius of the top circle (18 inches) and a measurement on the side (15 inches). We need either the height or the radius for an accurate calculation.
If we assume that the given measurement on the side (15 inches) is the height of the cylinder, we can proceed with the calculation. To find the lateral surface area, we can use the formula:
Lateral Surface Area = 2πrh
Given:
Radius (r) = 18 inches
Height (h) = 15 inches
Step 1: Calculate the lateral surface area:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2(3.14)(18)(15)
Lateral Surface Area ≈ 1696.4 square inches
Rounding this to the nearest whole number, the lateral surface area of the cylinder is approximately 1696 square inches.
To find the lateral surface area of a cylinder, you need to calculate the area of the curved surface that wraps around the sides of the cylinder.
The formula to find the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2πrh
Where:
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder's top circle
- h is the height of the cylinder
In the given information, it is stated that the top circle has a diameter of 18 inches. To find the radius (r), we divide the diameter by 2:
r = 18 in / 2 = 9 in
The information also states that there is a 15-inch measurement on the side. This represents the height (h) of the cylinder.
Now, let's plug these values into the formula to calculate the lateral surface area:
Lateral Surface Area = 2π(9 in)(15 in)
Using a calculator to evaluate this expression:
Lateral Surface Area ≈ 2(3.14159)(9)(15)
Lateral Surface Area ≈ 847.79 square inches
Rounding this value to the nearest whole number:
Lateral Surface Area ≈ 848 square inches
Therefore, the lateral surface area of the cylinder is approximately 848 square inches.