Part A
Find the lateral surface area of a cylinder with a radius of 2.5 meters and a height of 7 meters.
Use 3.14 for pi and round your answer to the nearest tenth.
(1 point)
m2
2
Question 2
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.
(1 point)
Responses
151.0 m2
151.0
2
151.0 m2
151.0
2
129.52 m2
129.52
2
129.52 m2
129.52
2
149.15 m2
149.15
2
149.15 m2
149.15
2
266.9 m2
Part A:
To find the lateral surface area of a cylinder, you need to calculate the perimeter of the base and multiply it by the height of the cylinder.
The perimeter of the base (which is a circle) can be found using the formula P = 2πr, where r is the radius of the base.
In this case, the radius is given as 2.5 meters.
So, the perimeter of the base is P = 2 * 3.14 * 2.5 = 15.7 meters.
Now, multiply the perimeter by the height of the cylinder (7 meters) to find the lateral surface area.
Lateral surface area = 15.7 * 7 = 109.9 square meters.
Rounded to the nearest tenth, the lateral surface area of the cylinder is approximately 109.9 square meters.
Answer: 109.9 m2.
Part B:
To find the total surface area of the cylinder, you need to consider both the lateral surface area and the areas of the two circular bases.
The lateral surface area has already been calculated in Part A as 109.9 square meters.
To find the area of one circular base, use the formula A = πr^2.
In this case, the radius is 2.5 meters.
So, the area of one circular base is A = 3.14 * (2.5)^2 = 19.625 square meters.
Since there are two circular bases, the total area of both bases is 2 * 19.625 = 39.25 square meters.
Now, add the lateral surface area and the areas of both bases to find the total surface area.
Total surface area = Lateral surface area + 2 * Area of one circular base
= 109.9 + 39.25
= 149.15 square meters.
Rounded to the nearest tenth, the total surface area of the cylinder is approximately 149.15 square meters.
Answer: 149.15 m2.