The radius of a cylinder is 3.5 ft. The height is 14 ft. Find the surface area and volume of the cylinder to the nearest tenth of a foot. Show your work. PLEaseeee Help
Certainly! To find the surface area and volume of a cylinder, we can use the following formulas:
1. The surface area of a cylinder is given by the formula: 2πr² + 2πrh, where r is the radius and h is the height.
2. The volume of a cylinder is given by the formula: πr²h.
Let's calculate the surface area first:
1. Surface Area:
- Given radius (r) = 3.5 ft
- Given height (h) = 14 ft
Using the formula, surface area = 2πr² + 2πrh, we can substitute the values:
surface area = 2π(3.5)² + 2π(3.5)(14)
surface area ≈ 2(3.14)(3.5)² + 2(3.14)(3.5)(14) [Using π ≈ 3.14]
Calculating further,
surface area ≈ 2(3.14)(12.25) + 2(3.14)(3.5)(14)
surface area ≈ 24.5(3.14) + 98(3.14)
surface area ≈ 76.93 + 307.12
surface area ≈ 384.05
Therefore, the surface area of the cylinder is approximately 384.05 square feet.
Now let's calculate the volume:
2. Volume:
- Given radius (r) = 3.5 ft
- Given height (h) = 14 ft
Using the formula, volume = πr²h, we can substitute the values:
volume = π(3.5)²(14)
volume ≈ (3.14)(3.5)²(14) [Using π ≈ 3.14]
Calculating further,
volume ≈ (3.14)(12.25)(14)
volume ≈ 430.34
Therefore, the volume of the cylinder is approximately 430.34 cubic feet.
So, the surface area is 384.05 square feet and the volume is 430.34 cubic feet, both to the nearest tenth of a foot.