A cylindrical container closed at both ends,has a radius of 3.5cm and a height of 8cm.calculate the total surface area of the container and volume of the container
just plug in your numbers:
S = 2πr(r+h)
V = πr^2 h
To calculate the total surface area of the container, we need to calculate the area of the two circular bases and the curved surface area.
1. Calculate the area of the circular bases:
The formula to calculate the area of a circle is A = π * r^2, where "A" is the area and "r" is the radius of the circle.
For the circular bases of the container, the radius is given as 3.5 cm, so we can calculate the area as follows:
Base area = π * (3.5 cm)^2
2. Calculate the curved surface area:
The formula to calculate the curved surface area of a cylinder is A = 2 * π * r * h, where "A" is the area, "r" is the radius, and "h" is the height of the cylinder.
For the curved surface area of the container, we can calculate it as follows:
Curved surface area = 2 * π * 3.5 cm * 8 cm
3. Calculate the total surface area:
The total surface area is the sum of the areas of the circular bases and the curved surface area.
Total surface area = 2 * base area + curved surface area
Now let's calculate the values:
1. Calculate the area of the circular bases:
Base area = π * (3.5 cm)^2
2. Calculate the curved surface area:
Curved surface area = 2 * π * 3.5 cm * 8 cm
3. Calculate the total surface area:
Total surface area = 2 * base area + curved surface area
To calculate the volume of the container, we can use the formula V = π * r^2 * h, where "V" is the volume, "r" is the radius, and "h" is the height of the cylinder.
4. Calculate the volume:
Volume = π * (3.5 cm)^2 * 8 cm
Let's calculate the values step-by-step:
1. Calculate the area of the circular bases:
Base area = π * (3.5 cm)^2
Base area = π * 12.25 cm^2
Base area ≈ 38.48 cm^2 (rounded to two decimal places)
2. Calculate the curved surface area:
Curved surface area = 2 * π * 3.5 cm * 8 cm
Curved surface area ≈ 175.93 cm^2 (rounded to two decimal places)
3. Calculate the total surface area:
Total surface area = 2 * base area + curved surface area
Total surface area = 2 * 38.48 cm^2 + 175.93 cm^2
Total surface area ≈ 252.89 cm^2 (rounded to two decimal places)
4. Calculate the volume:
Volume = π * (3.5 cm)^2 * 8 cm
Volume ≈ 308.92 cm^3 (rounded to two decimal places)
Therefore, the total surface area of the container is approximately 252.89 cm^2 and the volume is approximately 308.92 cm^3.
To calculate the total surface area of the container, we need to find the areas of the two circular bases and the lateral surface area.
1. Area of the circular bases:
The formula to find the area of a circle is A = πr², where "A" is the area and "r" is the radius.
Given that the radius (r) of the container is 3.5 cm, the area of one circular base is:
A₁ = π(3.5)²
2. Lateral surface area:
The lateral surface area of a cylinder is given by the formula A = 2πrh, where "A" is the area, "r" is the radius, and "h" is the height.
Given that the radius (r) of the container is 3.5 cm and the height (h) is 8 cm, the lateral surface area is:
A₂ = 2π(3.5)(8)
To calculate the total surface area, sum up the areas of the circular bases and the lateral surface area:
Total Surface Area = A₁ + A₁ + A₂
To calculate the volume of the container, we need to multiply the area of the circular base by the height of the cylinder.
1. Volume of the cylinder:
The formula to calculate the volume of a cylinder is V = πr²h, where "V" represents the volume, "r" is the radius, and "h" is the height.
Given that the radius (r) of the container is 3.5 cm and the height (h) is 8 cm, the volume of the cylinder is:
V = π(3.5)²(8)
To find the values of the total surface area and volume, simply substitute the known values into the respective formulas and perform the calculations.