A right cylinder has the radius of 5 centimeters and height of 22 centimeters.
Round to the nearest tenth.
I need to find -
Find Lateral Area
and
Find Surface area
recall that lateral area (area on the sides, not the top or the bottom) of a cylinder is given by,
LA = 2πrh
where
r = radius
h = height
π = "pi" equal to 3.14 (constant)
substituting,
LA = 2*(3.14)*5*22
LA = 690.8 cm^2
recall that the surface area of cylinder is the sum of the lateral area and area of the base, given by
SA = 2πrh + 2πr^2
where
r = radius
h = height
π = "pi" equal to 3.14 (constant)
substituting,
SA = 2*(3.14)*5*22 + 2*(3.14)*5^2
SA = 847.8 cm^2
hope this helps~ :)
Thank you so much!
Well, well, well, seems like we have a cylinder here! Let's get those calculations rolling.
To find the lateral area of a cylinder, we need to find the circumference of the base and then multiply it by the height. The formula for the lateral area is: Lateral Area = 2πrh.
Using the given numbers, we have a radius of 5 cm and a height of 22 cm. Plugging these values into the formula, we get:
Lateral Area = 2π(5 cm)(22 cm)
Now, let's use the value of π (pi) which is approximately 3.14 to calculate:
Lateral Area ≈ 2(3.14)(5 cm)(22 cm)
Doing the math, we get the lateral area of approximately 690.8 square centimeters.
Now, onto the surface area of the cylinder. To find this, we need to add the area of the two bases to the lateral area. The formula for the surface area is: Surface Area = 2πrh + 2πr².
Plugging in the values, we get:
Surface Area = 2π(5 cm)(22 cm) + 2π(5 cm)²
Calculating this, we have:
Surface Area ≈ 2(3.14)(5 cm)(22 cm) + 2(3.14)(5 cm)²
After crunching the numbers, we find that the surface area is approximately 976.8 square centimeters.
Remember, my friend, we rounded to the nearest tenth as requested.
To find the lateral area and surface area of a right cylinder, you can use the following formulas:
Lateral Area = 2 * π * radius * height
Surface Area = 2 * π * radius * (radius + height)
Given that the radius is 5 centimeters and the height is 22 centimeters, we can substitute these values into the formulas:
Lateral Area = 2 * π * 5 cm * 22 cm
Surface Area = 2 * π * 5 cm * (5 cm + 22 cm)
Now, we can calculate the values:
Lateral Area = 2 * 3.14 * 5 cm * 22 cm
Lateral Area ≈ 6.28 * 5 cm * 22 cm
Lateral Area ≈ 314 cm² (rounded to the nearest tenth)
Surface Area = 2 * 3.14 * 5 cm * (5 cm + 22 cm)
Surface Area ≈ 6.28 * 5 cm * 27 cm
Surface Area ≈ 848.52 cm² (rounded to the nearest tenth)
Therefore, the lateral area of the cylinder is approximately 314 cm², and the surface area is approximately 848.52 cm².
To find the lateral area and surface area of a right cylinder, you need to know its radius and height.
1. Lateral Area:
The lateral area refers to the curved surface area of the cylinder, excluding the top and bottom circles. The formula for the lateral area of a cylinder is given by:
Lateral Area = 2 * π * radius * height
In this case, the radius is 5 centimeters and the height is 22 centimeters. Plugging these values into the formula:
Lateral Area = 2 * π * 5 * 22
Lateral Area = 220 * π
Lateral Area ≈ 691.15 cm² (rounded to the nearest tenth)
Therefore, the lateral area of the cylinder is approximately 691.15 square centimeters.
2. Surface Area:
The surface area of a cylinder includes both the lateral area and the area of the two circular bases. The formula for the surface area of a cylinder is given by:
Surface Area = 2 * π * radius * height + 2 * π * radius^2
In this case, the radius is 5 centimeters and the height is 22 centimeters. Plugging these values into the formula:
Surface Area = 2 * π * 5 * 22 + 2 * π * 5^2
Surface Area = 220 * π + 50 * π
Surface Area ≈ 959.32 cm² (rounded to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 959.32 square centimeters.