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.
the SArea of the outer cylinder wall is PI*2*r*h
if the ends are enclosed, then you have to add two ends, or 2x PI*2r
A=2*pi*r*h+2*pi*r^2 <-Use this formula for your problem. :)
and volume is pi r^2 h
To find the surface area of a cylinder, you need to calculate the area of the two bases and the lateral surface area and then add them together.
1. Calculate the area of the bases:
- The base of the cylinder is a circle with radius 3.5 ft.
- The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
- Plugging in the values, we get A_base = π(3.5^2).
2. Calculate the lateral surface area:
- The lateral surface area of a cylinder is the curved surface area excluding the bases.
- The formula for the lateral surface area is A_lateral = 2πrh, where r represents the radius and h represents the height.
- Plugging in the values, we get A_lateral = 2π(3.5)(14).
3. Calculate the total surface area:
- The formula for the total surface area is A_total = 2A_base + A_lateral.
- Plugging in the values, we get A_total = 2(π(3.5^2)) + 2π(3.5)(14).
To find the volume of a cylinder, you need to calculate the area of the base and then multiply it by the height.
4. Calculate the volume:
- The formula for the volume of a cylinder is V = A_base * h.
- Plugging in the values, we get V = π(3.5^2)(14).
Now, let's calculate the surface area and volume of the given cylinder:
- Surface Area: A_total = 2(π(3.5^2)) + 2π(3.5)(14)
- Volume: V = π(3.5^2)(14)
Calculating the surface area and volume using a calculator or computer, the surface area is approximately 329.867 square feet (rounded to the nearest tenth) and the volume is approximately 539.753 cubic feet (rounded to the nearest tenth).