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.
Just use the formulas
area = two bases plus lateral = 2πr^2 + 2πrh
volume = base * height = πr^2 h
Just plug in the numbers
To find the surface area of a cylinder, we need to calculate the area of the two bases and the lateral surface area.
1. Base Area:
The base of a cylinder is a circle, and the formula for the area of a circle is A = π*r^2 (where r is the radius).
Given that the radius is 3.5 ft, we can calculate the base area of the cylinder:
Base Area = π*(3.5 ft)^2
Base Area ≈ 38.48 ft^2 (rounded to the nearest tenth)
2. Lateral Surface Area:
The lateral surface area (excluding the bases) of a cylinder can be found using the formula A = 2πrh (where r is the radius, and h is the height).
Given that the radius is 3.5 ft and the height is 14 ft, we can calculate the lateral surface area of the cylinder:
Lateral Surface Area = 2π*(3.5 ft)*(14 ft)
Lateral Surface Area ≈ 308.88 ft^2 (rounded to the nearest tenth)
3. Total Surface Area:
The total surface area of a cylinder is the sum of the base area and the lateral surface area.
Total Surface Area = 2(Base Area) + Lateral Surface Area
Total Surface Area ≈ 2(38.48 ft^2) + 308.88 ft^2
Total Surface Area ≈ 385.84 ft^2 (rounded to the nearest tenth)
Now, let's calculate the volume of the cylinder:
4. Volume:
The volume of a cylinder can be found using the formula V = π*r^2*h.
Given that the radius is 3.5 ft and the height is 14 ft, we can calculate the volume of the cylinder:
Volume = π*(3.5 ft)^2*(14 ft)
Volume ≈ 539.32 ft^3 (rounded to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 385.8 ft^2, and the volume is approximately 539.3 ft^3.
To find the surface area and volume of a cylinder, we will use the following formulas:
Surface Area = 2πrh + 2πr^2
Volume = πr^2h
Given that the radius (r) of the cylinder is 3.5 ft and the height (h) is 14 ft, we can substitute these values into the formulas to calculate the surface area and volume.
Surface Area = 2π(3.5)(14) + 2π(3.5)^2
Volume = π(3.5)^2(14)
Calculating these formulas step by step:
Surface Area = 2π(3.5)(14) + 2π(3.5)^2
= 98π + 2π(12.25)
= 98π + 24.5π
= 122.5π ft^2
To find the value of π, we can approximate it to 3.14.
Surface Area ≈ 122.5 * 3.14
≈ 384.85 ft^2 (rounded to the nearest tenth)
Now, let's calculate the volume:
Volume = π(3.5)^2(14)
= π(12.25)(14)
= 171.5π ft^3
Again, let's approximate π to 3.14.
Volume ≈ 171.5 * 3.14
≈ 538.61 ft^3 (rounded to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 384.9 square feet, and the volume is approximately 538.6 cubic feet.