Final answer:
To find the external surface area of a cylinder tire, calculate twice the area of its end caps and the area of the side surface. The total surface area for a cylinder with a radius of 4 feet and height of 3 feet is approximately 175.9 square feet.
Step-by-step explanation:
To calculate the surface area of the outside of a cylinder (which in this case is being used as a tire), you need to find the area of two types of surfaces: the circular top and bottom (end-caps) and the rectangular side that wraps around. The formula for the area of a circle is A = πr², where π is approximately 3.1415927 and 'r' is the radius. The cylinder has two circles, so you would calculate this twice. The side surface is a rectangle when unwrapped, and its area is found by multiplying the perimeter of the end caps, which is the circumference of the circle (2πr), by the height 'h' of the cylinder.
For this tire, with radius 4 feet and height 3 feet, the calculation would be as follows:
- The area for both end caps: 2π(4 ft)² = 2π(16 ft²) = 32π ft².
- The area of the side (rectangle): 2π(4 ft) × 3 ft = 24π ft².
- Total surface area = area of the end caps + area of the side = 32π ft² + 24π ft² = 56π ft².
Using π as approximately 3.1415927, you get:
56π ft² ≈ 56 × 3.1415927 ft² ≈ 175.9 ft².
Therefore, the surface area of the outside of the tire is approximately 175.9 square feet, rounded to the nearest tenth.