The radius of a cylinder is 3.5ft . The height is 14ft . Find the surface area and volume of the cylinder to the nearest tenth of a foot . Explain
Helppp!!!!
sides = circumference * height = 2 pi (3.5)(14)
top and bottom= 2 * pi(3.5)(3.5)
volume = pi r^2 h = pi (3.5)(3.5)(14)
To find the surface area of a cylinder, we need to find the area of the two bases and the lateral surface area.
1. The area of the base can be calculated using the formula for the area of a circle, which is A = π * r^2, where "r" is the radius.
Given that the radius of the cylinder is 3.5ft, the area of each base is A = π * (3.5)^2.
2. The lateral surface area of the cylinder can be found using the formula L = 2πrh, where "r" is the radius and "h" is the height.
Given that the radius is 3.5ft and the height is 14ft, the lateral surface area is L = 2π * 3.5 * 14.
3. The surface area is the sum of the base areas and the lateral surface area. Therefore, the total surface area of the cylinder is SA = 2A + L.
To calculate the volume of a cylinder, we use the formula V = π * r^2 * h, where "r" is the radius and "h" is the height.
Given that the radius is 3.5ft and the height is 14ft, the volume of the cylinder is V = π * (3.5)^2 * 14.
Now, let's calculate the surface area and the volume:
1. Area of each base:
A = π * (3.5)^2
A ≈ 38.48 ft^2
2. Lateral surface area:
L = 2π * 3.5 * 14
L ≈ 308.17 ft^2
3. Total surface area:
SA = 2A + L
SA = 2(38.48) + 308.17
SA ≈ 385.13 ft^2
4. Volume:
V = π * (3.5)^2 * 14
V ≈ 539.29 ft^3
Therefore, the surface area of the cylinder is approximately 385.13 square feet, and the volume is approximately 539.29 cubic feet.
To find the surface area of the cylinder, we need to add the areas of the two circular bases and the lateral surface area.
1. First, let's find the area of one circular base. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Plugging in the given radius, we have A_base = π(3.5ft)^2
2. Since there are two circular bases, the total base area will be twice the area of one base. So, A_total_base = 2 * A_base.
3. Next, let's find the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is A_lateral = 2πrh, where r is the radius and h is the height of the cylinder.
Plugging in the given values, we have A_lateral = 2 * π * 3.5ft * 14ft.
4. Finally, to find the total surface area, we add the total base area to the lateral surface area. So, A_total_surface = A_total_base + A_lateral.
Now, let's calculate the surface area:
A_base = π(3.5ft)^2
≈ 38.48 ft^2
A_total_base = 2 * A_base
≈ 76.96 ft^2
A_lateral = 2 * π * 3.5ft * 14ft
≈ 308.88 ft^2
A_total_surface = A_total_base + A_lateral
≈ 385.84 ft^2
To find the volume of the cylinder, we use the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
1. Plugging in the given values, we have V = π * (3.5ft)^2 * 14ft.
Now, let's calculate the volume:
V = π * (3.5ft)^2 * 14ft
≈ 539.86 ft^3
Therefore, the surface area of the cylinder is approximately 385.84 square feet, and the volume is approximately 539.86 cubic feet.