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.
you have r and h, so use your formulas:
v = π r^2 h
a = 2πr(r+h)
To find the surface area of a cylinder, we need to calculate the sum of the areas of the two circular bases and the lateral surface area.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
Given:
Radius (r) = 3.5 ft
Height (h) = 14 ft
First, let's calculate the area of the circular base:
Base Area = πr²
Substituting the value of the radius (r = 3.5 ft) into the formula, we get:
Base Area = π(3.5)²
Next, let's calculate the area of the lateral surface (the curved part):
Lateral Surface Area = 2πrh
Substituting the values of the radius (r = 3.5 ft) and height (h = 14 ft) into the formula, we get:
Lateral Surface Area = 2π(3.5)(14)
Now, let's calculate the total surface area:
Surface Area = 2πr² + 2πrh
Surface Area = 2π(3.5)² + 2π(3.5)(14)
To find the volume of a cylinder, we use the formula:
Volume = πr²h
Substituting the values of the radius (r = 3.5 ft) and height (h = 14 ft) into the formula, we get:
Volume = π(3.5)²(14)
Now, let's substitute the values into the formulas and calculate the surface area and volume:
Base Area = π(3.5)²
Base Area ≈ 38.48 ft² (rounded to the nearest tenth)
Lateral Surface Area = 2π(3.5)(14)
Lateral Surface Area ≈ 307.86 ft² (rounded to the nearest tenth)
Surface Area = 2π(3.5)² + 2π(3.5)(14)
Surface Area ≈ 384.76 ft² (rounded to the nearest tenth)
Volume = π(3.5)²(14)
Volume ≈ 539.13 ft³ (rounded to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 384.8 square feet, and the volume is approximately 539.1 cubic feet.