Calculate the surface area of a cylindrical steel bar which is 8 cm long and 3.5cm in diameter
two circular ends: πr^2 each
curved area: 2πrL
To calculate the surface area of a cylinder, you need to find the lateral area and the base area.
1. Lateral Area:
The lateral area of a cylinder can be calculated by multiplying the height of the cylinder by the perimeter of the base, which is the circumference of the circular base. The formula for the lateral area (LA) is LA = 2πrh, where r is the radius and h is the height.
Given:
Height (h) = 8 cm
Diameter (d) = 3.5 cm
The radius (r) of the cylinder can be found by dividing the diameter by 2: r = d/2 = 3.5 cm / 2 = 1.75 cm.
Now we can calculate the lateral area:
LA = 2πrh = 2π(1.75 cm)(8 cm) = 2(3.14)(1.75 cm)(8 cm) = 3.14 * 1.75 * 8 cm^2 ≈ 43.96 cm^2
2. Base Area:
The base area of a cylinder is given by the formula: BA = πr^2, where r is the radius.
Using the previously calculated radius (r = 1.75 cm), we can find the base area:
BA = πr^2 = π(1.75 cm)^2 = 3.14 * (1.75 cm)^2 ≈ 9.62 cm^2
3. Total Surface Area:
The total surface area (SA) of a cylinder is the sum of the lateral area and twice the base area. The formula is SA = 2πrh + 2πr^2.
Using the values calculated earlier, we can find the total surface area:
SA = 2πrh + 2πr^2 = 2(3.14)(1.75 cm)(8 cm) + 2(3.14)(1.75 cm)^2 ≈ 43.96 cm^2 + 9.62 cm^2 ≈ 53.58 cm^2
Therefore, the surface area of the given cylindrical steel bar is approximately 53.58 square centimeters.
To calculate the surface area of a cylindrical steel bar, you need to find the area of both the curved surface (lateral surface area) and the two circular bases.
To start, let's calculate the lateral surface area of the cylindrical bar.
The formula for the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2 * π * r * h
Where:
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder
- h is the height or length of the cylinder
In this case, the length of the cylindrical bar is given as 8 cm, but we need to find the radius.
The radius (r) is half the diameter of the cylindrical bar, which is given as 3.5 cm. So, the radius is 3.5 cm / 2 = 1.75 cm.
Now, we can substitute the values into the formula:
Lateral Surface Area = 2 * π * 1.75 cm * 8 cm
Lateral Surface Area = 11.08 cm^2
Next, let's calculate the area of the two circular bases.
The formula for the area of a circle is given by:
Base Area = π * r^2
Substituting the radius (r = 1.75 cm) into the formula:
Base Area = π * (1.75 cm)^2
Base Area = 9.62 cm^2
Since there are two bases, we need to multiply the base area by 2 to find the total area for both bases:
Total Base Area = 2 * 9.62 cm^2
Total Base Area = 19.24 cm^2
Finally, to find the surface area of the cylindrical steel bar, we add the lateral surface area and the total base area:
Surface Area = Lateral Surface Area + Total Base Area
Surface Area = 11.08 cm^2 + 19.24 cm^2
Surface Area = 30.32 cm^2
Therefore, the surface area of the given cylindrical steel bar is 30.32 square centimeters.