Question
surface area of cylinders QuickChek find the surface area of the cylinder use the approximation 3.14 for pi 7 yards 8 yards
Answers
GPT 3.5
To find the surface area of a cylinder, you need to calculate the sum of the areas of the two bases and the lateral surface area.
First, let's calculate the area of the bases. Since the bases of a cylinder are circles, you can use the formula A = πr², where A is the area and r is the radius.
The radius of the cylinder is half of the diameter, so it is 7/2 = 3.5 yards.
Area of one base = π × (3.5 yards)² = 3.14 × 3.5² = 3.14 × 12.25 = 38.465 square yards
Since there are two bases, the total area of the bases is 2 × 38.465 = 76.93 square yards.
Next, let's calculate the lateral surface area. The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height.
The height of the cylinder is given as 8 yards.
Lateral surface area = 2 × 3.14 × (3.5 yards) × (8 yards) = 2 × 3.14 × 3.5 × 8 = 175.36 square yards
Finally, the total surface area of the cylinder is the sum of the areas of the bases and the lateral surface area.
Total surface area = 76.93 square yards + 175.36 square yards = 252.29 square yards
Therefore, the surface area of the cylinder is approximately 252.29 square yards.
First, let's calculate the area of the bases. Since the bases of a cylinder are circles, you can use the formula A = πr², where A is the area and r is the radius.
The radius of the cylinder is half of the diameter, so it is 7/2 = 3.5 yards.
Area of one base = π × (3.5 yards)² = 3.14 × 3.5² = 3.14 × 12.25 = 38.465 square yards
Since there are two bases, the total area of the bases is 2 × 38.465 = 76.93 square yards.
Next, let's calculate the lateral surface area. The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height.
The height of the cylinder is given as 8 yards.
Lateral surface area = 2 × 3.14 × (3.5 yards) × (8 yards) = 2 × 3.14 × 3.5 × 8 = 175.36 square yards
Finally, the total surface area of the cylinder is the sum of the areas of the bases and the lateral surface area.
Total surface area = 76.93 square yards + 175.36 square yards = 252.29 square yards
Therefore, the surface area of the cylinder is approximately 252.29 square yards.