a cylinder has a base diameter of 8cm and a height of 12cm calculate
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To calculate the properties of a cylinder, we need to find its volume and surface area.
1. Finding the Volume of the Cylinder:
The formula to find the volume of a cylinder is given by:
Volume = π * r^2 * h
where π is a constant (approximately equal to 3.14159), r is the radius of the base, and h is the height of the cylinder.
Given that the base diameter is 8 cm, we can calculate the radius as:
Radius = diameter / 2 = 8 cm / 2 = 4 cm
Now, substituting the values into the formula, we have:
Volume = π * (4 cm)^2 * 12 cm
Volume = 3.14159 * 16 cm^2 * 12 cm
Volume ≈ 602.88 cm^3 (rounded to two decimal places)
Therefore, the volume of the cylinder is approximately 602.88 cm^3.
2. Finding the Surface Area of the Cylinder:
The formula to find the surface area of a cylinder is given by:
Surface Area = 2πr^2 + 2πrh
where π is a constant (approximately equal to 3.14159), r is the radius of the base, and h is the height of the cylinder.
Using the values provided, we can substitute them into the formula:
Surface Area = 2π * (4 cm)^2 + 2π * 4 cm * 12 cm
Surface Area = 2π * 16 cm^2 + 2π * 48 cm^2
Surface Area ≈ 301.59 cm^2 (rounded to two decimal places)
Therefore, the surface area of the cylinder is approximately 301.59 cm^2.
To calculate the volume of a cylinder, you need to use the formula:
Volume = π * r^2 * h
Where:
- π (pi) is a mathematical constant, approximately equal to 3.14159.
- r is the radius of the base of the cylinder.
- h is the height of the cylinder.
In this case, you are given the diameter of the base, which is 8cm. To find the radius, you divide the diameter by 2:
radius = diameter / 2
radius = 8cm / 2
radius = 4cm
Now, you have the radius (r) as 4cm and the height (h) as 12cm. Plug these values into the volume formula:
Volume = π * r^2 * h
Volume = 3.14159 * (4cm)^2 * 12cm
Volume = 3.14159 * 16cm^2 * 12cm
Volume = 3.14159 * 192cm^3
Volume ≈ 603.1858cm^3 (approximate to four decimal places)
Therefore, the volume of the cylinder with a base diameter of 8cm and a height of 12cm is approximately 603.1858cm^3.