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.
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To find the surface area and volume of a cylinder, we can use the following formulas:
1. Surface area of a cylinder: S = 2πrh + 2πr²
2. Volume of a cylinder: V = πr²h
Given that the radius (r) of the cylinder is 3.5 ft and the height (h) is 14 ft, let's calculate the surface area and volume.
Surface area of the cylinder (S):
Using the formula S = 2πrh + 2πr², substitute the values:
S = 2π(3.5)(14) + 2π(3.5)²
Calculating, we have:
S = 2(3.14)(3.5)(14) + 2(3.14)(3.5)²
S ≈ 219.8 ft² (rounded to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 219.8 ft².
Volume of the cylinder (V):
Using the formula V = πr²h, substitute the values:
V = π(3.5)²(14)
Calculating, we have:
V = (3.14)(3.5)²(14)
V ≈ 538.8 ft³ (rounded to the nearest tenth)
Therefore, the volume of the cylinder is approximately 538.8 ft³.
surface area:
A=2*π*r*h + 2*π*r^2
volume:
V=π*r^2*h
Those are the formulas; just plug in the numbers.
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