What is the surface area of a cylinder with a diameter of 4 cm and height of 6 cm?

To find the surface area of a cylinder, you need to calculate the area of both the curved surface and the areas of the two circular bases. The formula for the total surface area ( A ) of a cylinder can be expressed as:

[ A = 2\pi r(h + r) ]

where:

• ( r ) is the radius of the cylinder,

• ( h ) is the height of the cylinder.

Given a diameter of 4 cm, the radius ( r ) would be half of that:

[ r = \frac{diameter}{2} = \frac{4 cm}{2} = 2 cm ]

The height ( h ) is provided as 6 cm.

Now substituting the values into the surface area formula:

[ A = 2\pi(2 cm)(6 cm + 2 cm) ]

[ A = 2\pi(2 cm)(8 cm) ]

[ A = 2\pi(16 cm^2) ]

[ A = 32\pi cm^2 ]

Using ( \pi ) approximately as 3.14:

[ A = 32 \times 3.14 \approx 100