Part B
What is the total surface area of the cylinder from Part A? (Radius is 2.5 meters and height is 7 meters).
Use 3.14 for pi.
Responses
149.15 m2
149.15 m2
- correct
129.52 m2
129.52 m2
- no response given
151.0 m2
151.0 m2
- no response given
266.9 m2
The correct answer is 149.15 m2.
show work
To find the total surface area of a cylinder, you need to calculate the lateral surface area and the base areas separately, and then sum them up.
1. Lateral Surface Area:
The lateral surface area of a cylinder is given by the formula 2πrh, where r is the radius and h is the height.
In this case, the radius is 2.5 meters and the height is 7 meters. So, the lateral surface area would be:
Lateral Surface Area = 2π(2.5)(7) = 35π m2 (rounded to two decimal places)
2. Base Areas:
The base area of a cylinder is given by the formula πr^2, where r is the radius.
In this case, the radius is 2.5 meters. So, each base area would be:
Base Area = π(2.5)^2 = 6.25π m2 (rounded to two decimal places)
Since a cylinder has two bases, the total base area would be:
Total Base Area = 2(6.25π) = 12.5π m2 (rounded to two decimal places)
3. Total Surface Area:
To find the total surface area, you need to sum up the lateral surface area and the total base area.
Total Surface Area = Lateral Surface Area + Total Base Area
Plugging in the values, we get:
Total Surface Area = 35π + 12.5π = 47.5π m2
Now, we can approximate the value by using the approximation π = 3.14.
Total Surface Area ≈ 47.5(3.14) = 149.15 m2
Therefore, the total surface area of the cylinder is approximately 149.15 m2.
can you shorten it
Certainly! Here's a shortened version:
1. Lateral Surface Area: 2πrh, where r is the radius and h is the height.
Lateral Surface Area ≈ 2(3.14)(2.5)(7) = 35π m2 ≈ 110.2 m2
2. Base Areas: πr^2, where r is the radius.
Each Base Area ≈ (3.14)(2.5)^2 = 6.25π m2 ≈ 19.625 m2
Total Base Area ≈ 2(6.25π) = 12.5π m2 ≈ 39.25 m2
3. Total Surface Area: Lateral Surface Area + Total Base Area
Total Surface Area ≈ 110.2 m2 + 39.25 m2 ≈ 149.45 m2
Therefore, the total surface area of the cylinder is approximately 149.45 m2.