Use the net to find the approximate surface area of the cylinder to the nearest square meter.
A cylinder and its corresponding net diagram are shown. The circular bases have a radius of 7 meters. The cylinder height is 11 meters.
A. 377 m2
B. 484 m2
C. 528 m2
D. 792 m2
To find the surface area of the cylinder, we need to find the area of the two circular bases and the lateral surface area.
The area of each circular base is πr^2, where r is the radius. In this case, r = 7 meters, so the area of each base is:
π(7)^2 = 49π ≈ 153.94 m^2
The lateral surface area is the area of the rectangle that makes up the curved surface of the cylinder. The length of the rectangle is the circumference of the base, which is 2πr, and the width is the height of the cylinder, which is 11 meters. So the lateral surface area is:
2πr * h = 2π(7) * 11 = 154π ≈ 484.4 m^2
Adding the areas of the two bases and the lateral surface area, we get:
153.94 + 153.94 + 484.4 ≈ 792.28 m^2
Rounding to the nearest square meter, the approximate surface area of the cylinder is 792 m^2. Therefore, the answer is D. 792 m2.
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To find the surface area of the cylinder, we need to calculate the area of the two circular bases and the lateral surface area.
1. The area of one circular base can be calculated using the formula for the area of a circle: A_circular_base = π * r^2, where π is a constant approximately equal to 3.14 and r is the radius of the base.
A_circular_base = 3.14 * (7^2) = 3.14 * 49 = 153.86 m^2
2. Since there are two circular bases, the total area of the circular bases is:
Total_area_circular_bases = 2 * A_circular_base = 2 * 153.86 = 307.72 m^2
3. The lateral surface area of the cylinder is the area of the rectangle formed by "unrolling" the curved surface onto a flat surface. The length of the rectangle is the circumference of the base, which can be found using the formula C = 2 * π * r. The height of the rectangle is the height of the cylinder, which is given as 11 meters.
C = 2 * 3.14 * 7 = 43.96 meters
Lateral_surface_area = C * height = 43.96 * 11 = 483.56 m^2
4. The total surface area of the cylinder is the sum of the areas of the circular bases and the lateral surface area:
Total_surface_area = Total_area_circular_bases + Lateral_surface_area
= 307.72 + 483.56
= 791.28 m^2
Since we need to approximate the surface area to the nearest square meter, the approximate surface area of the cylinder is 791 m^2.
Therefore, the correct answer is D. 792 m^2.
To find the surface area of a cylinder, you need to add the areas of the two circular bases and the lateral surface area.
The formula to find the area of a circle is A = πr^2, where A represents the area and r is the radius of the circle.
First, let's find the area of one circular base. Since the radius of the circular base is 7 meters, the area of one base is A = π(7^2) = 49π square meters.
Now, let's find the lateral surface area. The lateral surface area of a cylinder is given by the formula LA = 2πrh, where LA represents the lateral surface area, r is the radius of the circular base, and h is the height of the cylinder.
In this case, the radius is 7 meters and the height is 11 meters, so the lateral surface area is LA = 2π(7)(11) = 154π square meters.
Now, let's add both the base area and the lateral surface area to find the total surface area. Total Surface Area = 2(Base Area) + Lateral Surface Area.
Total Surface Area = 2(49π) + 154π = 98π + 154π = 252π square meters.
To find the approximate surface area to the nearest square meter, we need to find the value of π and round the answer. The commonly used approximation for π is 3.14.
So, approximate surface area = 252π square meters ≈ 252 x 3.14 square meters ≈ 791.28 square meters.
Rounding this to the nearest square meter, the approximate surface area of the cylinder is 791 square meters.
Therefore, the correct answer is option D) 792 m2.