A cylinder has a height of 10cm and a diameter of 8cm.calculate its total surface area and its volume
To calculate the total surface area of the cylinder, we need to find the area of the two bases and the lateral surface area.
The area of each base is given by the formula for the area of a circle: A = πr^2, where r is the radius of the base. As the diameter is given as 8cm, the radius is half of that, so r = 8/2 = 4cm.
The area of one base is: A_base = π(4cm)^2 = 16π cm^2.
The lateral surface area can be calculated by multiplying the circumference of the base (2πr) by the height.
The circumference of the base is: C = 2πr = 2π(4cm) = 8π cm.
The lateral surface area is: A_lateral = C * height = 8π cm * 10 cm = 80π cm^2.
Finally, the total surface area is the sum of the areas of the two bases and the lateral surface area: A_total = 2A_base + A_lateral = 2(16π cm^2) + 80π cm^2 = 32π cm^2 + 80π cm^2 = 112π cm^2.
To calculate the volume of the cylinder, we use the formula V = πr^2h, where r is the radius of the base and h is the height.
The volume is: V = π(4cm)^2 * 10cm = 160π cm^3.
Therefore, the total surface area of the cylinder is 112π cm^2, and its volume is 160π cm^3.
To calculate the total surface area and volume of a cylinder, we will use the following formulas:
Total Surface Area of a Cylinder = 2πr(r + h)
Volume of a Cylinder = πr^2h
Given:
Height (h) = 10 cm
Diameter (d) = 8 cm
First, we need to find the radius (r) of the cylinder:
Radius (r) = diameter (d) / 2
= 8 cm / 2
= 4 cm
Now, we can substitute the values into the formulas to find the total surface area and volume:
Total Surface Area of a Cylinder = 2πr(r + h)
= 2 * π * 4 cm * (4 cm + 10 cm)
= 2π * 4 cm * 14 cm
= 112π cm^2
≈ 351.86 cm^2 (rounded to two decimal places)
Volume of a Cylinder = πr^2h
= π * (4 cm)^2 * 10 cm
= π * 16 cm^2 * 10 cm
= 160π cm^3
≈ 502.65 cm^3 (rounded to two decimal places)
Therefore, the total surface area of the cylinder is approximately 351.86 cm^2, and the volume of the cylinder is approximately 502.65 cm^3.